Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.2s

Alternatives: 9

Speedup: 1.0×

• 34.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 69.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 8200000000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.55e+113)
     t_1
     (if (<= y -4.4e-150)
       (* z (- x t))
       (if (<= y 8200000000000.0) (- x (* z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1.55e+113) {
		tmp = t_1;
	} else if (y <= -4.4e-150) {
		tmp = z * (x - t);
	} else if (y <= 8200000000000.0) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-1.55d+113)) then
        tmp = t_1
    else if (y <= (-4.4d-150)) then
        tmp = z * (x - t)
    else if (y <= 8200000000000.0d0) then
        tmp = x - (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1.55e+113) {
		tmp = t_1;
	} else if (y <= -4.4e-150) {
		tmp = z * (x - t);
	} else if (y <= 8200000000000.0) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -1.55e+113:
		tmp = t_1
	elif y <= -4.4e-150:
		tmp = z * (x - t)
	elif y <= 8200000000000.0:
		tmp = x - (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -1.55e+113)
		tmp = t_1;
	elseif (y <= -4.4e-150)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= 8200000000000.0)
		tmp = Float64(x - Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -1.55e+113)
		tmp = t_1;
	elseif (y <= -4.4e-150)
		tmp = z * (x - t);
	elseif (y <= 8200000000000.0)
		tmp = x - (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+113], t$95$1, If[LessEqual[y, -4.4e-150], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8200000000000.0], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999996e113 or 8.2e12 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 85.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 85.8%

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

   if -1.54999999999999996e113 < y < -4.3999999999999999e-150

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 72.8%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 72.8%

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

   if -4.3999999999999999e-150 < y < 8.2e12

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 83.8%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(t \cdot z\right)}\right) \]

      4. *-lowering-*.f64 77.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 77.5%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 8200000000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -2 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= (- y z) -2e-80) t_1 (if (<= (- y z) 5e-13) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -2e-80) {
		tmp = t_1;
	} else if ((y - z) <= 5e-13) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if ((y - z) <= (-2d-80)) then
        tmp = t_1
    else if ((y - z) <= 5d-13) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -2e-80) {
		tmp = t_1;
	} else if ((y - z) <= 5e-13) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if (y - z) <= -2e-80:
		tmp = t_1
	elif (y - z) <= 5e-13:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (Float64(y - z) <= -2e-80)
		tmp = t_1;
	elseif (Float64(y - z) <= 5e-13)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if ((y - z) <= -2e-80)
		tmp = t_1;
	elseif ((y - z) <= 5e-13)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -2e-80], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 5e-13], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -1.99999999999999992e-80 or 4.9999999999999999e-13 < (-.f64 y z)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 60.4%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 60.4%

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

   if -1.99999999999999992e-80 < (-.f64 y z) < 4.9999999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   7. Step-by-step derivation

   8. Simplified 68.1%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -2 \cdot 10^{-80}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+16}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x (- z y)))))
   (if (<= x -4.8e+14) t_1 (if (<= x 3.5e+16) (+ x (* (- y z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * (z - y));
	double tmp;
	if (x <= -4.8e+14) {
		tmp = t_1;
	} else if (x <= 3.5e+16) {
		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 = x + (x * (z - y))
    if (x <= (-4.8d+14)) then
        tmp = t_1
    else if (x <= 3.5d+16) 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 = x + (x * (z - y));
	double tmp;
	if (x <= -4.8e+14) {
		tmp = t_1;
	} else if (x <= 3.5e+16) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * (z - y))
	tmp = 0
	if x <= -4.8e+14:
		tmp = t_1
	elif x <= 3.5e+16:
		tmp = x + ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * Float64(z - y)))
	tmp = 0.0
	if (x <= -4.8e+14)
		tmp = t_1;
	elseif (x <= 3.5e+16)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * (z - y));
	tmp = 0.0;
	if (x <= -4.8e+14)
		tmp = t_1;
	elseif (x <= 3.5e+16)
		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[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+14], t$95$1, If[LessEqual[x, 3.5e+16], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8e14 or 3.5e16 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 81.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 81.1%

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

   if -4.8e14 < x < 3.5e16

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 88.4%

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -950000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-26}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x (- z y)))))
   (if (<= x -950000000.0) t_1 (if (<= x 8e-26) (* (- y z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * (z - y));
	double tmp;
	if (x <= -950000000.0) {
		tmp = t_1;
	} else if (x <= 8e-26) {
		tmp = (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 = x + (x * (z - y))
    if (x <= (-950000000.0d0)) then
        tmp = t_1
    else if (x <= 8d-26) then
        tmp = (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 = x + (x * (z - y));
	double tmp;
	if (x <= -950000000.0) {
		tmp = t_1;
	} else if (x <= 8e-26) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * (z - y))
	tmp = 0
	if x <= -950000000.0:
		tmp = t_1
	elif x <= 8e-26:
		tmp = (y - z) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * Float64(z - y)))
	tmp = 0.0
	if (x <= -950000000.0)
		tmp = t_1;
	elseif (x <= 8e-26)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * (z - y));
	tmp = 0.0;
	if (x <= -950000000.0)
		tmp = t_1;
	elseif (x <= 8e-26)
		tmp = (y - z) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -950000000.0], t$95$1, If[LessEqual[x, 8e-26], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5e8 or 8.0000000000000003e-26 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 79.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 79.8%

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

   if -9.5e8 < x < 8.0000000000000003e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 81.3%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 81.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -950000000:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-26}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 50000000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -7e+111) t_1 (if (<= y 50000000000.0) (* z (- x t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -7e+111) {
		tmp = t_1;
	} else if (y <= 50000000000.0) {
		tmp = z * (x - 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 * (t - x)
    if (y <= (-7d+111)) then
        tmp = t_1
    else if (y <= 50000000000.0d0) then
        tmp = z * (x - 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 * (t - x);
	double tmp;
	if (y <= -7e+111) {
		tmp = t_1;
	} else if (y <= 50000000000.0) {
		tmp = z * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -7e+111:
		tmp = t_1
	elif y <= 50000000000.0:
		tmp = z * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -7e+111)
		tmp = t_1;
	elseif (y <= 50000000000.0)
		tmp = Float64(z * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -7e+111)
		tmp = t_1;
	elseif (y <= 50000000000.0)
		tmp = z * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+111], t$95$1, If[LessEqual[y, 50000000000.0], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000004e111 or 5e10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 85.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 85.8%

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

   if -7.0000000000000004e111 < y < 5e10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 67.9%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 67.9%

      \[\leadsto \color{blue}{z \cdot \left(x - t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+27}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.25e+113) t_1 (if (<= y 4.3e+27) (* (- y z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1.25e+113) {
		tmp = t_1;
	} else if (y <= 4.3e+27) {
		tmp = (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 * (t - x)
    if (y <= (-1.25d+113)) then
        tmp = t_1
    else if (y <= 4.3d+27) then
        tmp = (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 * (t - x);
	double tmp;
	if (y <= -1.25e+113) {
		tmp = t_1;
	} else if (y <= 4.3e+27) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -1.25e+113:
		tmp = t_1
	elif y <= 4.3e+27:
		tmp = (y - z) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -1.25e+113)
		tmp = t_1;
	elseif (y <= 4.3e+27)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -1.25e+113)
		tmp = t_1;
	elseif (y <= 4.3e+27)
		tmp = (y - z) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+113], t$95$1, If[LessEqual[y, 4.3e+27], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e113 or 4.30000000000000008e27 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 87.1%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 87.1%

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

   if -1.25e113 < y < 4.30000000000000008e27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 58.6%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 58.6%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+27}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-46}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-46) (* y t) (if (<= y 2.9e-11) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-46) {
		tmp = y * t;
	} else if (y <= 2.9e-11) {
		tmp = x;
	} else {
		tmp = y * 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 (y <= (-1.6d-46)) then
        tmp = y * t
    else if (y <= 2.9d-11) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-46) {
		tmp = y * t;
	} else if (y <= 2.9e-11) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-46:
		tmp = y * t
	elif y <= 2.9e-11:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-46)
		tmp = Float64(y * t);
	elseif (y <= 2.9e-11)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e-46)
		tmp = y * t;
	elseif (y <= 2.9e-11)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-46], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.9e-11], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e-46 or 2.9e-11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 76.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 76.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{t}\right) \]
   7. Step-by-step derivation

   8. Simplified 41.2%

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

   if -1.6e-46 < y < 2.9e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 82.1%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   7. Step-by-step derivation

   8. Simplified 29.9%

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

Alternative 9: 18.3% 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 100.0%

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

3. Taylor expanded in t around inf

   \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
4. Step-by-step derivation

5. Simplified 68.9%

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

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
7. Step-by-step derivation

8. Simplified 15.7%

   \[\leadsto \color{blue}{x} \]
9. Add Preprocessing

Developer Target 1: 96.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024140 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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