Development.Shake.Progress:message from shake-0.15.5

Percentage Accurate: 99.5% → 99.7%

Time: 3.8s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (/ 100.0 (+ x y))))

C

double code(double x, double y) {
	return x * (100.0 / (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (100.0d0 / (x + y))
end function

Java

public static double code(double x, double y) {
	return x * (100.0 / (x + y));
}

Python

def code(x, y):
	return x * (100.0 / (x + y))

Julia

function code(x, y)
	return Float64(x * Float64(100.0 / Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (100.0 / (x + y));
end

Wolfram

code[x_, y_] := N[(x * N[(100.0 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\frac{x \cdot 100}{x + y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-un-lft-identity 99.7%

      \[\leadsto \frac{x \cdot 100}{\color{blue}{1 \cdot \left(x + y\right)}} \]

   2. times-frac 99.8%

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{100}{x + y}} \]

   3. +-commutative 99.8%

      \[\leadsto \frac{x}{1} \cdot \frac{100}{\color{blue}{y + x}} \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{100}{y + x}} \]

5. Final simplification 99.8%

   \[\leadsto x \cdot \frac{100}{x + y} \]
6. Add Preprocessing

Alternative 2: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+58} \lor \neg \left(y \leq -3800000000000 \lor \neg \left(y \leq -9 \cdot 10^{-15}\right) \land y \leq 4.4 \cdot 10^{+105}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.35e+58)
         (not
          (or (<= y -3800000000000.0)
              (and (not (<= y -9e-15)) (<= y 4.4e+105)))))
   (* 100.0 (/ x y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.35e+58) || !((y <= -3800000000000.0) || (!(y <= -9e-15) && (y <= 4.4e+105)))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.35d+58)) .or. (.not. (y <= (-3800000000000.0d0)) .or. (.not. (y <= (-9d-15))) .and. (y <= 4.4d+105))) then
        tmp = 100.0d0 * (x / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.35e+58) || !((y <= -3800000000000.0) || (!(y <= -9e-15) && (y <= 4.4e+105)))) {
		tmp = 100.0 * (x / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.35e+58) or not ((y <= -3800000000000.0) or (not (y <= -9e-15) and (y <= 4.4e+105))):
		tmp = 100.0 * (x / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.35e+58) || !((y <= -3800000000000.0) || (!(y <= -9e-15) && (y <= 4.4e+105))))
		tmp = Float64(100.0 * Float64(x / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.35e+58) || ~(((y <= -3800000000000.0) || (~((y <= -9e-15)) && (y <= 4.4e+105)))))
		tmp = 100.0 * (x / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.35e+58], N[Not[Or[LessEqual[y, -3800000000000.0], And[N[Not[LessEqual[y, -9e-15]], $MachinePrecision], LessEqual[y, 4.4e+105]]]], $MachinePrecision]], N[(100.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.34999999999999986e58 or -3.8e12 < y < -8.9999999999999995e-15 or 4.40000000000000014e105 < y

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 97.5%

         \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]

      3. +-commutative 97.5%

         \[\leadsto \frac{100}{\frac{\color{blue}{y + x}}{x}} \]

      4. remove-double-neg 97.5%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 97.5%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 97.5%

         \[\leadsto \frac{100}{\color{blue}{\frac{y}{x} - \frac{-x}{x}}} \]

      7. distribute-frac-neg 97.5%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 97.5%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 97.5%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{-1}} \]

   3. Simplified 97.5%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 85.3%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]

   if -2.34999999999999986e58 < y < -3.8e12 or -8.9999999999999995e-15 < y < 4.40000000000000014e105

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]

      3. +-commutative 99.9%

         \[\leadsto \frac{100}{\frac{\color{blue}{y + x}}{x}} \]

      4. remove-double-neg 99.9%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.9%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.9%

         \[\leadsto \frac{100}{\color{blue}{\frac{y}{x} - \frac{-x}{x}}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{-1}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{100} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+58} \lor \neg \left(y \leq -3800000000000 \lor \neg \left(y \leq -9 \cdot 10^{-15}\right) \land y \leq 4.4 \cdot 10^{+105}\right):\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+57} \lor \neg \left(y \leq -7800000000 \lor \neg \left(y \leq -1.1 \cdot 10^{-13}\right) \land y \leq 2.7 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.7e+57)
         (not
          (or (<= y -7800000000.0)
              (and (not (<= y -1.1e-13)) (<= y 2.7e+105)))))
   (* x (/ 100.0 y))
   100.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.7e+57) || !((y <= -7800000000.0) || (!(y <= -1.1e-13) && (y <= 2.7e+105)))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-5.7d+57)) .or. (.not. (y <= (-7800000000.0d0)) .or. (.not. (y <= (-1.1d-13))) .and. (y <= 2.7d+105))) then
        tmp = x * (100.0d0 / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5.7e+57) || !((y <= -7800000000.0) || (!(y <= -1.1e-13) && (y <= 2.7e+105)))) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.7e+57) or not ((y <= -7800000000.0) or (not (y <= -1.1e-13) and (y <= 2.7e+105))):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.7e+57) || !((y <= -7800000000.0) || (!(y <= -1.1e-13) && (y <= 2.7e+105))))
		tmp = Float64(x * Float64(100.0 / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5.7e+57) || ~(((y <= -7800000000.0) || (~((y <= -1.1e-13)) && (y <= 2.7e+105)))))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.7e+57], N[Not[Or[LessEqual[y, -7800000000.0], And[N[Not[LessEqual[y, -1.1e-13]], $MachinePrecision], LessEqual[y, 2.7e+105]]]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]

Derivation

1. Split input into 2 regimes

2. if y < -5.6999999999999998e57 or -7.8e9 < y < -1.09999999999999998e-13 or 2.70000000000000016e105 < y

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 97.5%

         \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]

      3. +-commutative 97.5%

         \[\leadsto \frac{100}{\frac{\color{blue}{y + x}}{x}} \]

      4. remove-double-neg 97.5%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 97.5%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 97.5%

         \[\leadsto \frac{100}{\color{blue}{\frac{y}{x} - \frac{-x}{x}}} \]

      7. distribute-frac-neg 97.5%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 97.5%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 97.5%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{-1}} \]

   3. Simplified 97.5%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 85.3%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 85.6%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

      2. *-commutative 85.6%

         \[\leadsto \frac{\color{blue}{x \cdot 100}}{y} \]

      3. associate-/l* 85.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]

   7. Simplified 85.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]
   8. Step-by-step derivation

      1. clear-num 83.3%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{y}{100}}{x}}} \]

      2. associate-/r/ 85.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{100}} \cdot x} \]

      3. clear-num 85.6%

         \[\leadsto \color{blue}{\frac{100}{y}} \cdot x \]

   9. Applied egg-rr 85.6%

      \[\leadsto \color{blue}{\frac{100}{y} \cdot x} \]

   if -5.6999999999999998e57 < y < -7.8e9 or -1.09999999999999998e-13 < y < 2.70000000000000016e105

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]

      3. +-commutative 99.9%

         \[\leadsto \frac{100}{\frac{\color{blue}{y + x}}{x}} \]

      4. remove-double-neg 99.9%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.9%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.9%

         \[\leadsto \frac{100}{\color{blue}{\frac{y}{x} - \frac{-x}{x}}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{-1}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{100} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+57} \lor \neg \left(y \leq -7800000000 \lor \neg \left(y \leq -1.1 \cdot 10^{-13}\right) \land y \leq 2.7 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;y \leq -72000000000000:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-14} \lor \neg \left(y \leq 2.7 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.5e+58)
   (/ x (/ y 100.0))
   (if (<= y -72000000000000.0)
     100.0
     (if (or (<= y -2.5e-14) (not (<= y 2.7e+105))) (* x (/ 100.0 y)) 100.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.5e+58) {
		tmp = x / (y / 100.0);
	} else if (y <= -72000000000000.0) {
		tmp = 100.0;
	} else if ((y <= -2.5e-14) || !(y <= 2.7e+105)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.5d+58)) then
        tmp = x / (y / 100.0d0)
    else if (y <= (-72000000000000.0d0)) then
        tmp = 100.0d0
    else if ((y <= (-2.5d-14)) .or. (.not. (y <= 2.7d+105))) then
        tmp = x * (100.0d0 / y)
    else
        tmp = 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.5e+58) {
		tmp = x / (y / 100.0);
	} else if (y <= -72000000000000.0) {
		tmp = 100.0;
	} else if ((y <= -2.5e-14) || !(y <= 2.7e+105)) {
		tmp = x * (100.0 / y);
	} else {
		tmp = 100.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.5e+58:
		tmp = x / (y / 100.0)
	elif y <= -72000000000000.0:
		tmp = 100.0
	elif (y <= -2.5e-14) or not (y <= 2.7e+105):
		tmp = x * (100.0 / y)
	else:
		tmp = 100.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.5e+58)
		tmp = Float64(x / Float64(y / 100.0));
	elseif (y <= -72000000000000.0)
		tmp = 100.0;
	elseif ((y <= -2.5e-14) || !(y <= 2.7e+105))
		tmp = Float64(x * Float64(100.0 / y));
	else
		tmp = 100.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.5e+58)
		tmp = x / (y / 100.0);
	elseif (y <= -72000000000000.0)
		tmp = 100.0;
	elseif ((y <= -2.5e-14) || ~((y <= 2.7e+105)))
		tmp = x * (100.0 / y);
	else
		tmp = 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.5e+58], N[(x / N[(y / 100.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -72000000000000.0], 100.0, If[Or[LessEqual[y, -2.5e-14], N[Not[LessEqual[y, 2.7e+105]], $MachinePrecision]], N[(x * N[(100.0 / y), $MachinePrecision]), $MachinePrecision], 100.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e58

   1. Initial program 99.8%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 98.3%

         \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]

      3. +-commutative 98.3%

         \[\leadsto \frac{100}{\frac{\color{blue}{y + x}}{x}} \]

      4. remove-double-neg 98.3%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 98.3%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 98.3%

         \[\leadsto \frac{100}{\color{blue}{\frac{y}{x} - \frac{-x}{x}}} \]

      7. distribute-frac-neg 98.3%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 98.3%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 98.3%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{-1}} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 83.5%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 83.6%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

      2. *-commutative 83.6%

         \[\leadsto \frac{\color{blue}{x \cdot 100}}{y} \]

      3. associate-/l* 83.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]

   7. Simplified 83.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]

   if -1.5000000000000001e58 < y < -7.2e13 or -2.5000000000000001e-14 < y < 2.70000000000000016e105

   1. Initial program 99.7%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]

      3. +-commutative 99.9%

         \[\leadsto \frac{100}{\frac{\color{blue}{y + x}}{x}} \]

      4. remove-double-neg 99.9%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 99.9%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 99.9%

         \[\leadsto \frac{100}{\color{blue}{\frac{y}{x} - \frac{-x}{x}}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 99.9%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{-1}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{100} \]

   if -7.2e13 < y < -2.5000000000000001e-14 or 2.70000000000000016e105 < y

   1. Initial program 99.6%

      \[\frac{x \cdot 100}{x + y} \]
   2. Step-by-step derivation

      1. *-commutative 99.6%

         \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

      2. associate-/l* 96.6%

         \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]

      3. +-commutative 96.6%

         \[\leadsto \frac{100}{\frac{\color{blue}{y + x}}{x}} \]

      4. remove-double-neg 96.6%

         \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

      5. unsub-neg 96.6%

         \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

      6. div-sub 96.6%

         \[\leadsto \frac{100}{\color{blue}{\frac{y}{x} - \frac{-x}{x}}} \]

      7. distribute-frac-neg 96.6%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

      8. *-inverses 96.6%

         \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

      9. metadata-eval 96.6%

         \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{-1}} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 87.4%

      \[\leadsto \color{blue}{100 \cdot \frac{x}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 87.8%

         \[\leadsto \color{blue}{\frac{100 \cdot x}{y}} \]

      2. *-commutative 87.8%

         \[\leadsto \frac{\color{blue}{x \cdot 100}}{y} \]

      3. associate-/l* 87.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]

   7. Simplified 87.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{100}}} \]
   8. Step-by-step derivation

      1. clear-num 84.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{y}{100}}{x}}} \]

      2. associate-/r/ 87.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{100}} \cdot x} \]

      3. clear-num 87.9%

         \[\leadsto \color{blue}{\frac{100}{y}} \cdot x \]

   9. Applied egg-rr 87.9%

      \[\leadsto \color{blue}{\frac{100}{y} \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{\frac{y}{100}}\\ \mathbf{elif}\;y \leq -72000000000000:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-14} \lor \neg \left(y \leq 2.7 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{100}{\frac{y}{x} - -1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 100.0 (- (/ y x) -1.0)))

C

double code(double x, double y) {
	return 100.0 / ((y / x) - -1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 100.0d0 / ((y / x) - (-1.0d0))
end function

Java

public static double code(double x, double y) {
	return 100.0 / ((y / x) - -1.0);
}

Python

def code(x, y):
	return 100.0 / ((y / x) - -1.0)

Julia

function code(x, y)
	return Float64(100.0 / Float64(Float64(y / x) - -1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = 100.0 / ((y / x) - -1.0);
end

Wolfram

code[x_, y_] := N[(100.0 / N[(N[(y / x), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\frac{x \cdot 100}{x + y} \]
2. Step-by-step derivation

   1. *-commutative 99.7%

      \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

   2. associate-/l* 99.0%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]

   3. +-commutative 99.0%

      \[\leadsto \frac{100}{\frac{\color{blue}{y + x}}{x}} \]

   4. remove-double-neg 99.0%

      \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

   5. unsub-neg 99.0%

      \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

   6. div-sub 99.0%

      \[\leadsto \frac{100}{\color{blue}{\frac{y}{x} - \frac{-x}{x}}} \]

   7. distribute-frac-neg 99.0%

      \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

   8. *-inverses 99.0%

      \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

   9. metadata-eval 99.0%

      \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{-1}} \]

3. Simplified 99.0%

   \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
4. Add Preprocessing

5. Final simplification 99.0%

   \[\leadsto \frac{100}{\frac{y}{x} - -1} \]
6. Add Preprocessing

Alternative 6: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\left(x + y\right) \cdot 0.01} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* (+ x y) 0.01)))

C

double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / ((x + y) * 0.01d0)
end function

Java

public static double code(double x, double y) {
	return x / ((x + y) * 0.01);
}

Python

def code(x, y):
	return x / ((x + y) * 0.01)

Julia

function code(x, y)
	return Float64(x / Float64(Float64(x + y) * 0.01))
end

MATLAB

function tmp = code(x, y)
	tmp = x / ((x + y) * 0.01);
end

Wolfram

code[x_, y_] := N[(x / N[(N[(x + y), $MachinePrecision] * 0.01), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\frac{x \cdot 100}{x + y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. expm1-log1p-u 97.8%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)\right)} \]

   2. expm1-udef 65.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot 100}{x + y}\right)} - 1} \]

   3. associate-/l* 65.6%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{x + y}{100}}}\right)} - 1 \]

   4. div-inv 65.6%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100}}}\right)} - 1 \]

   5. +-commutative 65.6%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{\left(y + x\right)} \cdot \frac{1}{100}}\right)} - 1 \]

   6. metadata-eval 65.6%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot \color{blue}{0.01}}\right)} - 1 \]

4. Applied egg-rr 65.6%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)} - 1} \]
5. Step-by-step derivation

   1. expm1-def 97.8%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\left(y + x\right) \cdot 0.01}\right)\right)} \]

   2. expm1-log1p 99.7%

      \[\leadsto \color{blue}{\frac{x}{\left(y + x\right) \cdot 0.01}} \]

6. Simplified 99.7%

   \[\leadsto \color{blue}{\frac{x}{\left(y + x\right) \cdot 0.01}} \]

7. Final simplification 99.7%

   \[\leadsto \frac{x}{\left(x + y\right) \cdot 0.01} \]
8. Add Preprocessing

Alternative 7: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))

C

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

Python

def code(x, y):
	return (x * 100.0) / (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\frac{x \cdot 100}{x + y} \]
2. Add Preprocessing

3. Final simplification 99.7%

   \[\leadsto \frac{x \cdot 100}{x + y} \]
4. Add Preprocessing

Alternative 8: 51.1% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 100 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 100.0)

C

double code(double x, double y) {
	return 100.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 100.0d0
end function

Java

public static double code(double x, double y) {
	return 100.0;
}

Python

def code(x, y):
	return 100.0

Julia

function code(x, y)
	return 100.0
end

MATLAB

function tmp = code(x, y)
	tmp = 100.0;
end

Wolfram

code[x_, y_] := 100.0

Derivation

1. Initial program 99.7%

   \[\frac{x \cdot 100}{x + y} \]
2. Step-by-step derivation

   1. *-commutative 99.7%

      \[\leadsto \frac{\color{blue}{100 \cdot x}}{x + y} \]

   2. associate-/l* 99.0%

      \[\leadsto \color{blue}{\frac{100}{\frac{x + y}{x}}} \]

   3. +-commutative 99.0%

      \[\leadsto \frac{100}{\frac{\color{blue}{y + x}}{x}} \]

   4. remove-double-neg 99.0%

      \[\leadsto \frac{100}{\frac{y + \color{blue}{\left(-\left(-x\right)\right)}}{x}} \]

   5. unsub-neg 99.0%

      \[\leadsto \frac{100}{\frac{\color{blue}{y - \left(-x\right)}}{x}} \]

   6. div-sub 99.0%

      \[\leadsto \frac{100}{\color{blue}{\frac{y}{x} - \frac{-x}{x}}} \]

   7. distribute-frac-neg 99.0%

      \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{\left(-\frac{x}{x}\right)}} \]

   8. *-inverses 99.0%

      \[\leadsto \frac{100}{\frac{y}{x} - \left(-\color{blue}{1}\right)} \]

   9. metadata-eval 99.0%

      \[\leadsto \frac{100}{\frac{y}{x} - \color{blue}{-1}} \]

3. Simplified 99.0%

   \[\leadsto \color{blue}{\frac{100}{\frac{y}{x} - -1}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 54.2%

   \[\leadsto \color{blue}{100} \]

6. Final simplification 54.2%

   \[\leadsto 100 \]
7. Add Preprocessing

Developer target: 99.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{1} \cdot \frac{100}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ x 1.0) (/ 100.0 (+ x y))))

C

double code(double x, double y) {
	return (x / 1.0) * (100.0 / (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / 1.0d0) * (100.0d0 / (x + y))
end function

Java

public static double code(double x, double y) {
	return (x / 1.0) * (100.0 / (x + y));
}

Python

def code(x, y):
	return (x / 1.0) * (100.0 / (x + y))

Julia

function code(x, y)
	return Float64(Float64(x / 1.0) * Float64(100.0 / Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x / 1.0) * (100.0 / (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x / 1.0), $MachinePrecision] * N[(100.0 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024021 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))