Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.7s

Alternatives: 13

Speedup: 1.0×

• 33.6% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := x - z \cdot t\\ \mathbf{if}\;y \leq -80000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-47}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-283}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 48000:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))) (t_2 (* y (- t x))) (t_3 (- x (* z t))))
   (if (<= y -80000000000000.0)
     t_2
     (if (<= y -8.5e-47)
       (* z (- x t))
       (if (<= y -2.6e-213)
         t_1
         (if (<= y 8.2e-283)
           t_3
           (if (<= y 5e-229) t_1 (if (<= y 48000.0) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = y * (t - x);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -80000000000000.0) {
		tmp = t_2;
	} else if (y <= -8.5e-47) {
		tmp = z * (x - t);
	} else if (y <= -2.6e-213) {
		tmp = t_1;
	} else if (y <= 8.2e-283) {
		tmp = t_3;
	} else if (y <= 5e-229) {
		tmp = t_1;
	} else if (y <= 48000.0) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x + (z * x)
    t_2 = y * (t - x)
    t_3 = x - (z * t)
    if (y <= (-80000000000000.0d0)) then
        tmp = t_2
    else if (y <= (-8.5d-47)) then
        tmp = z * (x - t)
    else if (y <= (-2.6d-213)) then
        tmp = t_1
    else if (y <= 8.2d-283) then
        tmp = t_3
    else if (y <= 5d-229) then
        tmp = t_1
    else if (y <= 48000.0d0) then
        tmp = t_3
    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 + (z * x);
	double t_2 = y * (t - x);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -80000000000000.0) {
		tmp = t_2;
	} else if (y <= -8.5e-47) {
		tmp = z * (x - t);
	} else if (y <= -2.6e-213) {
		tmp = t_1;
	} else if (y <= 8.2e-283) {
		tmp = t_3;
	} else if (y <= 5e-229) {
		tmp = t_1;
	} else if (y <= 48000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	t_2 = y * (t - x)
	t_3 = x - (z * t)
	tmp = 0
	if y <= -80000000000000.0:
		tmp = t_2
	elif y <= -8.5e-47:
		tmp = z * (x - t)
	elif y <= -2.6e-213:
		tmp = t_1
	elif y <= 8.2e-283:
		tmp = t_3
	elif y <= 5e-229:
		tmp = t_1
	elif y <= 48000.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -80000000000000.0)
		tmp = t_2;
	elseif (y <= -8.5e-47)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= -2.6e-213)
		tmp = t_1;
	elseif (y <= 8.2e-283)
		tmp = t_3;
	elseif (y <= 5e-229)
		tmp = t_1;
	elseif (y <= 48000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	t_2 = y * (t - x);
	t_3 = x - (z * t);
	tmp = 0.0;
	if (y <= -80000000000000.0)
		tmp = t_2;
	elseif (y <= -8.5e-47)
		tmp = z * (x - t);
	elseif (y <= -2.6e-213)
		tmp = t_1;
	elseif (y <= 8.2e-283)
		tmp = t_3;
	elseif (y <= 5e-229)
		tmp = t_1;
	elseif (y <= 48000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -80000000000000.0], t$95$2, If[LessEqual[y, -8.5e-47], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-213], t$95$1, If[LessEqual[y, 8.2e-283], t$95$3, If[LessEqual[y, 5e-229], t$95$1, If[LessEqual[y, 48000.0], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8e13 or 48000 < 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 83.6%

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

      1. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in y around inf 83.5%

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

   if -8e13 < y < -8.4999999999999999e-47

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in z around inf 82.5%

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

   if -8.4999999999999999e-47 < y < -2.6000000000000001e-213 or 8.19999999999999973e-283 < y < 5.00000000000000016e-229

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-rgt-neg-in 78.1%

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

      3. neg-sub0 78.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 78.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 78.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 78.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 78.1%

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

      8. remove-double-neg 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around inf 78.1%

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

   if -2.6000000000000001e-213 < y < 8.19999999999999973e-283 or 5.00000000000000016e-229 < y < 48000

   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 82.1%

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

   4. Taylor expanded in y around 0 73.9%

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

      1. associate-*r* 73.9%

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

      2. neg-mul-1 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -80000000000000:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-47}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-213}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-283}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-229}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 48000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-128}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-69}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 0.032:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* z (- x t))) (t_3 (* y (- t x))))
   (if (<= z -1.6e+15)
     t_2
     (if (<= z -6.2e-128)
       t_3
       (if (<= z 1.05e-172)
         t_1
         (if (<= z 2.2e-69) t_3 (if (<= z 0.032) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * (x - t);
	double t_3 = y * (t - x);
	double tmp;
	if (z <= -1.6e+15) {
		tmp = t_2;
	} else if (z <= -6.2e-128) {
		tmp = t_3;
	} else if (z <= 1.05e-172) {
		tmp = t_1;
	} else if (z <= 2.2e-69) {
		tmp = t_3;
	} else if (z <= 0.032) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = z * (x - t)
    t_3 = y * (t - x)
    if (z <= (-1.6d+15)) then
        tmp = t_2
    else if (z <= (-6.2d-128)) then
        tmp = t_3
    else if (z <= 1.05d-172) then
        tmp = t_1
    else if (z <= 2.2d-69) then
        tmp = t_3
    else if (z <= 0.032d0) 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 * (1.0 - y);
	double t_2 = z * (x - t);
	double t_3 = y * (t - x);
	double tmp;
	if (z <= -1.6e+15) {
		tmp = t_2;
	} else if (z <= -6.2e-128) {
		tmp = t_3;
	} else if (z <= 1.05e-172) {
		tmp = t_1;
	} else if (z <= 2.2e-69) {
		tmp = t_3;
	} else if (z <= 0.032) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = z * (x - t)
	t_3 = y * (t - x)
	tmp = 0
	if z <= -1.6e+15:
		tmp = t_2
	elif z <= -6.2e-128:
		tmp = t_3
	elif z <= 1.05e-172:
		tmp = t_1
	elif z <= 2.2e-69:
		tmp = t_3
	elif z <= 0.032:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (z <= -1.6e+15)
		tmp = t_2;
	elseif (z <= -6.2e-128)
		tmp = t_3;
	elseif (z <= 1.05e-172)
		tmp = t_1;
	elseif (z <= 2.2e-69)
		tmp = t_3;
	elseif (z <= 0.032)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = z * (x - t);
	t_3 = y * (t - x);
	tmp = 0.0;
	if (z <= -1.6e+15)
		tmp = t_2;
	elseif (z <= -6.2e-128)
		tmp = t_3;
	elseif (z <= 1.05e-172)
		tmp = t_1;
	elseif (z <= 2.2e-69)
		tmp = t_3;
	elseif (z <= 0.032)
		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[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+15], t$95$2, If[LessEqual[z, -6.2e-128], t$95$3, If[LessEqual[z, 1.05e-172], t$95$1, If[LessEqual[z, 2.2e-69], t$95$3, If[LessEqual[z, 0.032], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e15 or 0.032000000000000001 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. unsub-neg 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in z around inf 83.9%

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

   if -1.6e15 < z < -6.20000000000000005e-128 or 1.05e-172 < z < 2.2e-69

   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 86.1%

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

      1. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in y around inf 69.9%

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

   if -6.20000000000000005e-128 < z < 1.05e-172 or 2.2e-69 < z < 0.032000000000000001

   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 95.1%

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

      1. *-commutative 95.1%

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

   5. Simplified 95.1%

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

   6. Taylor expanded in x around inf 73.4%

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

      1. neg-mul-1 73.4%

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

      2. unsub-neg 73.4%

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

   8. Simplified 73.4%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 0.032:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 0.07:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* y (- t x))))
   (if (<= z -1.5e+16)
     t_1
     (if (<= z -1.7e-142)
       t_2
       (if (<= z 1.35e-171)
         (- x (* y x))
         (if (<= z 5.8e-69) t_2 (if (<= z 0.07) (* x (- 1.0 y)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (z <= -1.5e+16) {
		tmp = t_1;
	} else if (z <= -1.7e-142) {
		tmp = t_2;
	} else if (z <= 1.35e-171) {
		tmp = x - (y * x);
	} else if (z <= 5.8e-69) {
		tmp = t_2;
	} else if (z <= 0.07) {
		tmp = x * (1.0 - y);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = y * (t - x)
    if (z <= (-1.5d+16)) then
        tmp = t_1
    else if (z <= (-1.7d-142)) then
        tmp = t_2
    else if (z <= 1.35d-171) then
        tmp = x - (y * x)
    else if (z <= 5.8d-69) then
        tmp = t_2
    else if (z <= 0.07d0) then
        tmp = x * (1.0d0 - y)
    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 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (z <= -1.5e+16) {
		tmp = t_1;
	} else if (z <= -1.7e-142) {
		tmp = t_2;
	} else if (z <= 1.35e-171) {
		tmp = x - (y * x);
	} else if (z <= 5.8e-69) {
		tmp = t_2;
	} else if (z <= 0.07) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = y * (t - x)
	tmp = 0
	if z <= -1.5e+16:
		tmp = t_1
	elif z <= -1.7e-142:
		tmp = t_2
	elif z <= 1.35e-171:
		tmp = x - (y * x)
	elif z <= 5.8e-69:
		tmp = t_2
	elif z <= 0.07:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (z <= -1.5e+16)
		tmp = t_1;
	elseif (z <= -1.7e-142)
		tmp = t_2;
	elseif (z <= 1.35e-171)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 5.8e-69)
		tmp = t_2;
	elseif (z <= 0.07)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = y * (t - x);
	tmp = 0.0;
	if (z <= -1.5e+16)
		tmp = t_1;
	elseif (z <= -1.7e-142)
		tmp = t_2;
	elseif (z <= 1.35e-171)
		tmp = x - (y * x);
	elseif (z <= 5.8e-69)
		tmp = t_2;
	elseif (z <= 0.07)
		tmp = x * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+16], t$95$1, If[LessEqual[z, -1.7e-142], t$95$2, If[LessEqual[z, 1.35e-171], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-69], t$95$2, If[LessEqual[z, 0.07], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5e16 or 0.070000000000000007 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. unsub-neg 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in z around inf 83.9%

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

   if -1.5e16 < z < -1.70000000000000014e-142 or 1.35000000000000007e-171 < z < 5.7999999999999997e-69

   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 86.1%

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

      1. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in y around inf 69.9%

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

   if -1.70000000000000014e-142 < z < 1.35000000000000007e-171

   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 74.2%

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

      1. mul-1-neg 74.2%

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

      2. distribute-rgt-neg-in 74.2%

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

      3. neg-sub0 74.2%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 74.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 74.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 74.2%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 74.2%

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

      8. remove-double-neg 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in z around 0 74.2%

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

      1. mul-1-neg 74.2%

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

      2. unsub-neg 74.2%

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

   8. Simplified 74.2%

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

   if 5.7999999999999997e-69 < z < 0.070000000000000007

   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 78.1%

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

      1. *-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in x around inf 69.7%

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

      1. neg-mul-1 69.7%

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

      2. unsub-neg 69.7%

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

   8. Simplified 69.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 0.07:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x - t \cdot \left(z - y\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-284}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-225}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 54000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (- x (* t (- z y)))))
   (if (<= y -8e+52)
     t_1
     (if (<= y 4.8e-284)
       t_2
       (if (<= y 4.7e-225) (+ x (* z x)) (if (<= y 54000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x - (t * (z - y));
	double tmp;
	if (y <= -8e+52) {
		tmp = t_1;
	} else if (y <= 4.8e-284) {
		tmp = t_2;
	} else if (y <= 4.7e-225) {
		tmp = x + (z * x);
	} else if (y <= 54000.0) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x - (t * (z - y))
    if (y <= (-8d+52)) then
        tmp = t_1
    else if (y <= 4.8d-284) then
        tmp = t_2
    else if (y <= 4.7d-225) then
        tmp = x + (z * x)
    else if (y <= 54000.0d0) then
        tmp = t_2
    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 t_2 = x - (t * (z - y));
	double tmp;
	if (y <= -8e+52) {
		tmp = t_1;
	} else if (y <= 4.8e-284) {
		tmp = t_2;
	} else if (y <= 4.7e-225) {
		tmp = x + (z * x);
	} else if (y <= 54000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x - (t * (z - y))
	tmp = 0
	if y <= -8e+52:
		tmp = t_1
	elif y <= 4.8e-284:
		tmp = t_2
	elif y <= 4.7e-225:
		tmp = x + (z * x)
	elif y <= 54000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x - Float64(t * Float64(z - y)))
	tmp = 0.0
	if (y <= -8e+52)
		tmp = t_1;
	elseif (y <= 4.8e-284)
		tmp = t_2;
	elseif (y <= 4.7e-225)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 54000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x - (t * (z - y));
	tmp = 0.0;
	if (y <= -8e+52)
		tmp = t_1;
	elseif (y <= 4.8e-284)
		tmp = t_2;
	elseif (y <= 4.7e-225)
		tmp = x + (z * x);
	elseif (y <= 54000.0)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+52], t$95$1, If[LessEqual[y, 4.8e-284], t$95$2, If[LessEqual[y, 4.7e-225], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 54000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9999999999999999e52 or 54000 < 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 84.2%

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

      1. *-commutative 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in y around inf 84.0%

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

   if -7.9999999999999999e52 < y < 4.80000000000000006e-284 or 4.70000000000000014e-225 < y < 54000

   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 77.5%

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

   if 4.80000000000000006e-284 < y < 4.70000000000000014e-225

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 100.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 100.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 100.0%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 100.0%

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

      8. remove-double-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-284}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-225}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 54000:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -84 \lor \neg \left(x \leq 0.0064\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -84.0) (not (<= x 0.0064)))
   (+ x (* x (- z y)))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -84.0) || !(x <= 0.0064)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x - (t * (z - y));
	}
	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 <= (-84.0d0)) .or. (.not. (x <= 0.0064d0))) then
        tmp = x + (x * (z - y))
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -84.0) || !(x <= 0.0064)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -84.0) or not (x <= 0.0064):
		tmp = x + (x * (z - y))
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -84.0) || !(x <= 0.0064))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -84.0) || ~((x <= 0.0064)))
		tmp = x + (x * (z - y));
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -84.0], N[Not[LessEqual[x, 0.0064]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -84 or 0.00640000000000000031 < 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 86.6%

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

      1. mul-1-neg 86.6%

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

      2. distribute-rgt-neg-in 86.6%

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

      3. neg-sub0 86.6%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 86.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 86.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 86.6%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 86.6%

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

      8. remove-double-neg 86.6%

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

   5. Simplified 86.6%

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

   if -84 < x < 0.00640000000000000031

   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 86.3%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -84 \lor \neg \left(x \leq 0.0064\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -145000000 \lor \neg \left(z \leq 200000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -145000000.0) (not (<= z 200000000000.0)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -145000000.0) || !(z <= 200000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - 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 <= (-145000000.0d0)) .or. (.not. (z <= 200000000000.0d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -145000000.0) || !(z <= 200000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -145000000.0) or not (z <= 200000000000.0):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -145000000.0) || !(z <= 200000000000.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -145000000.0) || ~((z <= 200000000000.0)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -145000000.0], N[Not[LessEqual[z, 200000000000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e8 or 2e11 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.8%

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

      1. mul-1-neg 82.8%

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

      2. unsub-neg 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in z around inf 82.8%

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

   if -1.45e8 < z < 2e11

   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 92.0%

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

      1. *-commutative 92.0%

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

   5. Simplified 92.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -145000000 \lor \neg \left(z \leq 200000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{-8}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;z \leq 38000000000000:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -2.65e-8)
     (+ x t_1)
     (if (<= z 38000000000000.0) (+ x (* y (- t x))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -2.65e-8) {
		tmp = x + t_1;
	} else if (z <= 38000000000000.0) {
		tmp = x + (y * (t - 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 = z * (x - t)
    if (z <= (-2.65d-8)) then
        tmp = x + t_1
    else if (z <= 38000000000000.0d0) then
        tmp = x + (y * (t - 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 = z * (x - t);
	double tmp;
	if (z <= -2.65e-8) {
		tmp = x + t_1;
	} else if (z <= 38000000000000.0) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -2.65e-8:
		tmp = x + t_1
	elif z <= 38000000000000.0:
		tmp = x + (y * (t - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -2.65e-8)
		tmp = Float64(x + t_1);
	elseif (z <= 38000000000000.0)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -2.65e-8)
		tmp = x + t_1;
	elseif (z <= 38000000000000.0)
		tmp = x + (y * (t - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.65e-8], N[(x + t$95$1), $MachinePrecision], If[LessEqual[z, 38000000000000.0], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6499999999999999e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   5. Simplified 81.4%

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

   if -2.6499999999999999e-8 < z < 3.8e13

   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 93.3%

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

      1. *-commutative 93.3%

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

   5. Simplified 93.3%

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

   if 3.8e13 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. unsub-neg 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in z around inf 82.5%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 38000000000000:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-29} \lor \neg \left(y \leq 52000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.4e-29) (not (<= y 52000.0))) (* y (- t x)) (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-29) || !(y <= 52000.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (1.0 - y);
	}
	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 <= (-4.4d-29)) .or. (.not. (y <= 52000.0d0))) then
        tmp = y * (t - x)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-29) || !(y <= 52000.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.4e-29) or not (y <= 52000.0):
		tmp = y * (t - x)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.4e-29) || !(y <= 52000.0))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.4e-29) || ~((y <= 52000.0)))
		tmp = y * (t - x);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.4e-29], N[Not[LessEqual[y, 52000.0]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.39999999999999981e-29 or 52000 < 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 79.6%

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

      1. *-commutative 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in y around inf 78.8%

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

   if -4.39999999999999981e-29 < y < 52000

   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 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in x around inf 36.2%

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

      1. neg-mul-1 36.2%

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

      2. unsub-neg 36.2%

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

   8. Simplified 36.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-29} \lor \neg \left(y \leq 52000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+20} \lor \neg \left(y \leq 55000\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.35e+20) (not (<= y 55000.0))) (* y (- x)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.35e+20) || !(y <= 55000.0)) {
		tmp = y * -x;
	} 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 ((y <= (-2.35d+20)) .or. (.not. (y <= 55000.0d0))) then
        tmp = y * -x
    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 ((y <= -2.35e+20) || !(y <= 55000.0)) {
		tmp = y * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.35e+20) or not (y <= 55000.0):
		tmp = y * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.35e+20) || !(y <= 55000.0))
		tmp = Float64(y * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.35e+20) || ~((y <= 55000.0)))
		tmp = y * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.35e+20], N[Not[LessEqual[y, 55000.0]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.35e20 or 55000 < 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 83.2%

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

      1. *-commutative 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in x around inf 46.1%

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

      1. neg-mul-1 46.1%

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

      2. unsub-neg 46.1%

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

   8. Simplified 46.1%

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

   9. Taylor expanded in y around inf 45.9%

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

       1. associate-*r* 45.9%

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

       2. neg-mul-1 45.9%

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

       3. *-commutative 45.9%

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

   11. Simplified 45.9%

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

   if -2.35e20 < y < 55000

   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 42.4%

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

      1. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   6. Taylor expanded in y around 0 32.9%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+20} \lor \neg \left(y \leq 55000\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 12: 38.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 y)))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - y);
}

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 * (1.0d0 - y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - y);
}

Python

def code(x, y, z, t):
	return x * (1.0 - y)

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - y);
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

Derivation

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 61.2%

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

   1. *-commutative 61.2%

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

5. Simplified 61.2%

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

6. Taylor expanded in x around inf 39.6%

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

   1. neg-mul-1 39.6%

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

   2. unsub-neg 39.6%

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

8. Simplified 39.6%

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

9. Final simplification 39.6%

   \[\leadsto x \cdot \left(1 - y\right) \]
10. Add Preprocessing

Alternative 13: 18.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 61.2%

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

   1. *-commutative 61.2%

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

5. Simplified 61.2%

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

6. Taylor expanded in y around 0 18.9%

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

7. Final simplification 18.9%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 96.2% 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 2024077 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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