Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.4% → 98.5%

Time: 7.9s

Alternatives: 10

Speedup: 1.0×

• 24.3% 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: 92.4% 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: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ z (/ t (- y x))))
     (if (<= t_1 2e+284) t_1 (+ x (* z (/ (- y x) t)))))))

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 / (t / (y - x)));
	} else if (t_1 <= 2e+284) {
		tmp = t_1;
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	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 / (t / (y - x)));
	} else if (t_1 <= 2e+284) {
		tmp = t_1;
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	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 / (t / (y - x)))
	elif t_1 <= 2e+284:
		tmp = t_1
	else:
		tmp = x + (z * ((y - x) / t))
	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(t / Float64(y - x))));
	elseif (t_1 <= 2e+284)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	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 / (t / (y - x)));
	elseif (t_1 <= 2e+284)
		tmp = t_1;
	else
		tmp = x + (z * ((y - x) / t));
	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[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+284], t$95$1, N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $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 78.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 2.00000000000000016e284

   1. Initial program 99.3%

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

   if 2.00000000000000016e284 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 79.1%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq 2 \cdot 10^{+284}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 2: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-90} \lor \neg \left(z \leq 2.2 \cdot 10^{-220} \lor \neg \left(z \leq 2.1 \cdot 10^{-204}\right) \land z \leq 2.1 \cdot 10^{-17}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.5e-90)
         (not (or (<= z 2.2e-220) (and (not (<= z 2.1e-204)) (<= z 2.1e-17)))))
   (* (- y x) (/ z t))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e-90) || !((z <= 2.2e-220) || (!(z <= 2.1e-204) && (z <= 2.1e-17)))) {
		tmp = (y - x) * (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 ((z <= (-3.5d-90)) .or. (.not. (z <= 2.2d-220) .or. (.not. (z <= 2.1d-204)) .and. (z <= 2.1d-17))) then
        tmp = (y - x) * (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 ((z <= -3.5e-90) || !((z <= 2.2e-220) || (!(z <= 2.1e-204) && (z <= 2.1e-17)))) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.5e-90) or not ((z <= 2.2e-220) or (not (z <= 2.1e-204) and (z <= 2.1e-17))):
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.5e-90) || !((z <= 2.2e-220) || (!(z <= 2.1e-204) && (z <= 2.1e-17))))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.5e-90) || ~(((z <= 2.2e-220) || (~((z <= 2.1e-204)) && (z <= 2.1e-17)))))
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.5e-90], N[Not[Or[LessEqual[z, 2.2e-220], And[N[Not[LessEqual[z, 2.1e-204]], $MachinePrecision], LessEqual[z, 2.1e-17]]]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999999e-90 or 2.19999999999999987e-220 < z < 2.10000000000000009e-204 or 2.09999999999999992e-17 < z

   1. Initial program 87.5%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 77.3%

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

   5. Taylor expanded in z around inf 61.2%

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

      1. associate-*r/ 61.2%

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

      2. neg-mul-1 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in x around 0 62.4%

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

      1. associate-*l/ 64.6%

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

      2. associate-*r* 64.6%

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

      3. neg-mul-1 64.6%

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

      4. associate-*l/ 67.0%

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

      5. distribute-rgt-in 74.8%

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

      6. +-commutative 74.8%

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

      7. unsub-neg 74.8%

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

      8. distribute-lft-out-- 67.0%

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

      9. associate-*r/ 64.6%

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

      10. associate-*l/ 68.2%

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

      11. associate-*r/ 65.4%

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

      12. associate-*l/ 66.1%

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

      13. distribute-lft-out-- 81.3%

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

   10. Simplified 81.3%

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

   if -3.4999999999999999e-90 < z < 2.19999999999999987e-220 or 2.10000000000000009e-204 < z < 2.09999999999999992e-17

   1. Initial program 99.0%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in t around inf 70.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-90} \lor \neg \left(z \leq 2.2 \cdot 10^{-220} \lor \neg \left(z \leq 2.1 \cdot 10^{-204}\right) \land z \leq 2.1 \cdot 10^{-17}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+76}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+153}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= z -3.5e+62)
     t_1
     (if (<= z 1.55e-32)
       (+ x (/ (* y z) t))
       (if (<= z 1.22e+76)
         (- x (* x (/ z t)))
         (if (<= z 3.25e+153) (+ x (* y (/ z t))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if (z <= -3.5e+62) {
		tmp = t_1;
	} else if (z <= 1.55e-32) {
		tmp = x + ((y * z) / t);
	} else if (z <= 1.22e+76) {
		tmp = x - (x * (z / t));
	} else if (z <= 3.25e+153) {
		tmp = x + (y * (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 - x) * (z / t)
    if (z <= (-3.5d+62)) then
        tmp = t_1
    else if (z <= 1.55d-32) then
        tmp = x + ((y * z) / t)
    else if (z <= 1.22d+76) then
        tmp = x - (x * (z / t))
    else if (z <= 3.25d+153) then
        tmp = x + (y * (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 - x) * (z / t);
	double tmp;
	if (z <= -3.5e+62) {
		tmp = t_1;
	} else if (z <= 1.55e-32) {
		tmp = x + ((y * z) / t);
	} else if (z <= 1.22e+76) {
		tmp = x - (x * (z / t));
	} else if (z <= 3.25e+153) {
		tmp = x + (y * (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	tmp = 0
	if z <= -3.5e+62:
		tmp = t_1
	elif z <= 1.55e-32:
		tmp = x + ((y * z) / t)
	elif z <= 1.22e+76:
		tmp = x - (x * (z / t))
	elif z <= 3.25e+153:
		tmp = x + (y * (z / t))
	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 (z <= -3.5e+62)
		tmp = t_1;
	elseif (z <= 1.55e-32)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (z <= 1.22e+76)
		tmp = Float64(x - Float64(x * Float64(z / t)));
	elseif (z <= 3.25e+153)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	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 (z <= -3.5e+62)
		tmp = t_1;
	elseif (z <= 1.55e-32)
		tmp = x + ((y * z) / t);
	elseif (z <= 1.22e+76)
		tmp = x - (x * (z / t));
	elseif (z <= 3.25e+153)
		tmp = x + (y * (z / t));
	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[z, -3.5e+62], t$95$1, If[LessEqual[z, 1.55e-32], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+76], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.25e+153], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.49999999999999984e62 or 3.24999999999999986e153 < z

   1. Initial program 84.5%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around 0 66.5%

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

   5. Taylor expanded in z around inf 58.8%

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

      1. associate-*r/ 58.8%

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

      2. neg-mul-1 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in x around 0 59.6%

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

      1. associate-*l/ 63.3%

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

      2. associate-*r* 63.3%

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

      3. neg-mul-1 63.3%

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

      4. associate-*l/ 70.0%

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

      5. distribute-rgt-in 83.2%

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

      6. +-commutative 83.2%

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

      7. unsub-neg 83.2%

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

      8. distribute-lft-out-- 70.0%

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

      9. associate-*r/ 63.3%

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

      10. associate-*l/ 69.3%

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

      11. associate-*r/ 64.6%

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

      12. associate-*l/ 66.8%

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

      13. distribute-lft-out-- 90.1%

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

   10. Simplified 90.1%

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

   if -3.49999999999999984e62 < z < 1.55000000000000005e-32

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 90.6%

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

      1. *-commutative 90.6%

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

   4. Simplified 90.6%

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

   if 1.55000000000000005e-32 < z < 1.22000000000000002e76

   1. Initial program 99.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 95.4%

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

      1. distribute-lft-in 95.4%

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

      2. mul-1-neg 95.4%

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

      3. distribute-rgt-neg-in 95.4%

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

      4. unsub-neg 95.4%

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

      5. *-rgt-identity 95.4%

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

   6. Simplified 95.4%

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

   if 1.22000000000000002e76 < z < 3.24999999999999986e153

   1. Initial program 72.0%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 71.4%

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

      1. associate-*r/ 82.5%

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

   6. Simplified 82.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+62}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+76}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+153}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]

Alternative 4: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := x - x \cdot \frac{z}{t}\\ \mathbf{if}\;x \leq -7 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))) (t_2 (- x (* x (/ z t)))))
   (if (<= x -7e+82)
     t_2
     (if (<= x -7e-36)
       t_1
       (if (<= x -3.8e-92)
         (/ (* (- y x) z) t)
         (if (<= x 1.25e+62) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double t_2 = x - (x * (z / t));
	double tmp;
	if (x <= -7e+82) {
		tmp = t_2;
	} else if (x <= -7e-36) {
		tmp = t_1;
	} else if (x <= -3.8e-92) {
		tmp = ((y - x) * z) / t;
	} else if (x <= 1.25e+62) {
		tmp = t_1;
	} 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 = x + (y * (z / t))
    t_2 = x - (x * (z / t))
    if (x <= (-7d+82)) then
        tmp = t_2
    else if (x <= (-7d-36)) then
        tmp = t_1
    else if (x <= (-3.8d-92)) then
        tmp = ((y - x) * z) / t
    else if (x <= 1.25d+62) then
        tmp = t_1
    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 = x + (y * (z / t));
	double t_2 = x - (x * (z / t));
	double tmp;
	if (x <= -7e+82) {
		tmp = t_2;
	} else if (x <= -7e-36) {
		tmp = t_1;
	} else if (x <= -3.8e-92) {
		tmp = ((y - x) * z) / t;
	} else if (x <= 1.25e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	t_2 = x - (x * (z / t))
	tmp = 0
	if x <= -7e+82:
		tmp = t_2
	elif x <= -7e-36:
		tmp = t_1
	elif x <= -3.8e-92:
		tmp = ((y - x) * z) / t
	elif x <= 1.25e+62:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(x - Float64(x * Float64(z / t)))
	tmp = 0.0
	if (x <= -7e+82)
		tmp = t_2;
	elseif (x <= -7e-36)
		tmp = t_1;
	elseif (x <= -3.8e-92)
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	elseif (x <= 1.25e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	t_2 = x - (x * (z / t));
	tmp = 0.0;
	if (x <= -7e+82)
		tmp = t_2;
	elseif (x <= -7e-36)
		tmp = t_1;
	elseif (x <= -3.8e-92)
		tmp = ((y - x) * z) / t;
	elseif (x <= 1.25e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+82], t$95$2, If[LessEqual[x, -7e-36], t$95$1, If[LessEqual[x, -3.8e-92], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, 1.25e+62], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.0000000000000001e82 or 1.25000000000000007e62 < x

   1. Initial program 89.8%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 91.5%

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

      1. distribute-lft-in 91.5%

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

      2. mul-1-neg 91.5%

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

      3. distribute-rgt-neg-in 91.5%

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

      4. unsub-neg 91.5%

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

      5. *-rgt-identity 91.5%

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

   6. Simplified 91.5%

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

   if -7.0000000000000001e82 < x < -6.9999999999999999e-36 or -3.8000000000000001e-92 < x < 1.25000000000000007e62

   1. Initial program 93.0%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around inf 84.3%

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

      1. associate-*r/ 88.9%

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

   6. Simplified 88.9%

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

   if -6.9999999999999999e-36 < x < -3.8000000000000001e-92

   1. Initial program 99.9%

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

      1. associate-*l/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around 0 94.0%

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

   5. Taylor expanded in z around inf 88.0%

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

      1. associate-*r/ 88.0%

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

      2. neg-mul-1 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in t around 0 93.9%

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

      1. mul-1-neg 93.9%

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

      2. distribute-lft-neg-out 93.9%

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

      3. +-commutative 93.9%

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

      4. distribute-rgt-out 93.9%

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

   10. Simplified 93.9%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+82}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-36}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+62}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 94.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-103} \lor \neg \left(z \leq 3.7 \cdot 10^{-94}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.45e-103) (not (<= z 3.7e-94)))
   (+ x (* z (/ (- y x) t)))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-103) || !(z <= 3.7e-94)) {
		tmp = x + (z * ((y - x) / 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 ((z <= (-1.45d-103)) .or. (.not. (z <= 3.7d-94))) then
        tmp = x + (z * ((y - x) / 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 ((z <= -1.45e-103) || !(z <= 3.7e-94)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.45e-103) or not (z <= 3.7e-94):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.45e-103) || !(z <= 3.7e-94))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.45e-103) || ~((z <= 3.7e-94)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.45e-103], N[Not[LessEqual[z, 3.7e-94]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4499999999999999e-103 or 3.6999999999999998e-94 < z

   1. Initial program 88.6%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   if -1.4499999999999999e-103 < z < 3.6999999999999998e-94

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 95.7%

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

      1. *-commutative 95.7%

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

   4. Simplified 95.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-103} \lor \neg \left(z \leq 3.7 \cdot 10^{-94}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 6: 94.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-103)
   (+ x (/ z (/ t (- y x))))
   (if (<= z 9e-95) (+ x (/ (* y z) t)) (+ x (* z (/ (- y x) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-103) {
		tmp = x + (z / (t / (y - x)));
	} else if (z <= 9e-95) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x + (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 (z <= (-7.5d-103)) then
        tmp = x + (z / (t / (y - x)))
    else if (z <= 9d-95) then
        tmp = x + ((y * z) / t)
    else
        tmp = x + (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 (z <= -7.5e-103) {
		tmp = x + (z / (t / (y - x)));
	} else if (z <= 9e-95) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-103:
		tmp = x + (z / (t / (y - x)))
	elif z <= 9e-95:
		tmp = x + ((y * z) / t)
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-103)
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	elseif (z <= 9e-95)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-103)
		tmp = x + (z / (t / (y - x)));
	elseif (z <= 9e-95)
		tmp = x + ((y * z) / t);
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-103], N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-95], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e-103

   1. Initial program 93.4%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

      1. *-commutative 96.6%

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

      2. clear-num 96.6%

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

      3. un-div-inv 96.6%

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

   5. Applied egg-rr 96.6%

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

   if -7.5e-103 < z < 9e-95

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 95.7%

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

      1. *-commutative 95.7%

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

   4. Simplified 95.7%

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

   if 9e-95 < z

   1. Initial program 83.5%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-95}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 7: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+62} \lor \neg \left(z \leq 1.74 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.3e+62) (not (<= z 1.74e-9)))
   (* (- y x) (/ z t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.3e+62) || !(z <= 1.74e-9)) {
		tmp = (y - 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 ((z <= (-4.3d+62)) .or. (.not. (z <= 1.74d-9))) then
        tmp = (y - 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 ((z <= -4.3e+62) || !(z <= 1.74e-9)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.3e+62) or not (z <= 1.74e-9):
		tmp = (y - x) * (z / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.3e+62) || !(z <= 1.74e-9))
		tmp = Float64(Float64(y - 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 ((z <= -4.3e+62) || ~((z <= 1.74e-9)))
		tmp = (y - x) * (z / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.3e+62], N[Not[LessEqual[z, 1.74e-9]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2999999999999997e62 or 1.73999999999999999e-9 < z

   1. Initial program 83.8%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around 0 71.4%

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

   5. Taylor expanded in z around inf 59.7%

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

      1. associate-*r/ 59.7%

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

      2. neg-mul-1 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in x around 0 61.2%

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

      1. associate-*l/ 64.1%

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

      2. associate-*r* 64.1%

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

      3. neg-mul-1 64.1%

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

      4. associate-*l/ 69.5%

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

      5. distribute-rgt-in 79.7%

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

      6. +-commutative 79.7%

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

      7. unsub-neg 79.7%

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

      8. distribute-lft-out-- 69.5%

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

      9. associate-*r/ 64.1%

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

      10. associate-*l/ 69.6%

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

      11. associate-*r/ 65.9%

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

      12. associate-*l/ 66.8%

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

      13. distribute-lft-out-- 85.7%

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

   10. Simplified 85.7%

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

   if -4.2999999999999997e62 < z < 1.73999999999999999e-9

   1. Initial program 99.2%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around inf 90.7%

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

      1. associate-*r/ 88.7%

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

   6. Simplified 88.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+62} \lor \neg \left(z \leq 1.74 \cdot 10^{-9}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 8: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+63} \lor \neg \left(z \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.56e+63) (not (<= z 5.8e-8)))
   (* (- y x) (/ z t))
   (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.56e+63) || !(z <= 5.8e-8)) {
		tmp = (y - 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 ((z <= (-1.56d+63)) .or. (.not. (z <= 5.8d-8))) then
        tmp = (y - 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 ((z <= -1.56e+63) || !(z <= 5.8e-8)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.56e+63) or not (z <= 5.8e-8):
		tmp = (y - x) * (z / t)
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.56e+63) || !(z <= 5.8e-8))
		tmp = Float64(Float64(y - x) * Float64(z / t));
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.56e+63) || ~((z <= 5.8e-8)))
		tmp = (y - x) * (z / t);
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.56e+63], N[Not[LessEqual[z, 5.8e-8]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.56e63 or 5.8000000000000003e-8 < z

   1. Initial program 83.8%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around 0 71.4%

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

   5. Taylor expanded in z around inf 59.7%

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

      1. associate-*r/ 59.7%

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

      2. neg-mul-1 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in x around 0 61.2%

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

      1. associate-*l/ 64.1%

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

      2. associate-*r* 64.1%

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

      3. neg-mul-1 64.1%

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

      4. associate-*l/ 69.5%

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

      5. distribute-rgt-in 79.7%

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

      6. +-commutative 79.7%

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

      7. unsub-neg 79.7%

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

      8. distribute-lft-out-- 69.5%

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

      9. associate-*r/ 64.1%

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

      10. associate-*l/ 69.6%

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

      11. associate-*r/ 65.9%

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

      12. associate-*l/ 66.8%

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

      13. distribute-lft-out-- 85.7%

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

   10. Simplified 85.7%

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

   if -1.56e63 < z < 5.8000000000000003e-8

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 90.7%

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

      1. *-commutative 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+63} \lor \neg \left(z \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]

Alternative 9: 97.8% 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 92.2%

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

   1. associate-/l* 98.1%

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

3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 10: 38.7% 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 92.2%

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

   1. associate-*l/ 91.9%

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

3. Simplified 91.9%

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

4. Taylor expanded in t around inf 39.3%

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

5. Final simplification 39.3%

   \[\leadsto x \]

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 2023271 
(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)))