Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 16

Speedup: 1.0×

• 34.2% 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. Add Preprocessing

Alternative 2: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-198}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-139}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* y (- t x))) (t_3 (* x (+ z 1.0))))
   (if (<= y -1.55e-20)
     t_2
     (if (<= y -2.75e-198)
       t_3
       (if (<= y -9.6e-288)
         t_1
         (if (<= y 1.65e-139)
           t_3
           (if (<= y 6.6e-105) t_1 (if (<= y 1.65e+14) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = y * (t - x);
	double t_3 = x * (z + 1.0);
	double tmp;
	if (y <= -1.55e-20) {
		tmp = t_2;
	} else if (y <= -2.75e-198) {
		tmp = t_3;
	} else if (y <= -9.6e-288) {
		tmp = t_1;
	} else if (y <= 1.65e-139) {
		tmp = t_3;
	} else if (y <= 6.6e-105) {
		tmp = t_1;
	} else if (y <= 1.65e+14) {
		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 = (y - z) * t
    t_2 = y * (t - x)
    t_3 = x * (z + 1.0d0)
    if (y <= (-1.55d-20)) then
        tmp = t_2
    else if (y <= (-2.75d-198)) then
        tmp = t_3
    else if (y <= (-9.6d-288)) then
        tmp = t_1
    else if (y <= 1.65d-139) then
        tmp = t_3
    else if (y <= 6.6d-105) then
        tmp = t_1
    else if (y <= 1.65d+14) 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 = (y - z) * t;
	double t_2 = y * (t - x);
	double t_3 = x * (z + 1.0);
	double tmp;
	if (y <= -1.55e-20) {
		tmp = t_2;
	} else if (y <= -2.75e-198) {
		tmp = t_3;
	} else if (y <= -9.6e-288) {
		tmp = t_1;
	} else if (y <= 1.65e-139) {
		tmp = t_3;
	} else if (y <= 6.6e-105) {
		tmp = t_1;
	} else if (y <= 1.65e+14) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = y * (t - x)
	t_3 = x * (z + 1.0)
	tmp = 0
	if y <= -1.55e-20:
		tmp = t_2
	elif y <= -2.75e-198:
		tmp = t_3
	elif y <= -9.6e-288:
		tmp = t_1
	elif y <= 1.65e-139:
		tmp = t_3
	elif y <= 6.6e-105:
		tmp = t_1
	elif y <= 1.65e+14:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -1.55e-20)
		tmp = t_2;
	elseif (y <= -2.75e-198)
		tmp = t_3;
	elseif (y <= -9.6e-288)
		tmp = t_1;
	elseif (y <= 1.65e-139)
		tmp = t_3;
	elseif (y <= 6.6e-105)
		tmp = t_1;
	elseif (y <= 1.65e+14)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = y * (t - x);
	t_3 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -1.55e-20)
		tmp = t_2;
	elseif (y <= -2.75e-198)
		tmp = t_3;
	elseif (y <= -9.6e-288)
		tmp = t_1;
	elseif (y <= 1.65e-139)
		tmp = t_3;
	elseif (y <= 6.6e-105)
		tmp = t_1;
	elseif (y <= 1.65e+14)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e-20], t$95$2, If[LessEqual[y, -2.75e-198], t$95$3, If[LessEqual[y, -9.6e-288], t$95$1, If[LessEqual[y, 1.65e-139], t$95$3, If[LessEqual[y, 6.6e-105], t$95$1, If[LessEqual[y, 1.65e+14], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e-20 or 1.65e14 < 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 83.9%

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

   if -1.55e-20 < y < -2.75e-198 or -9.5999999999999994e-288 < y < 1.65e-139 or 6.5999999999999997e-105 < y < 1.65e14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. unsub-neg 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in y around 0 66.5%

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

      1. +-commutative 66.5%

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

   8. Simplified 66.5%

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

   if -2.75e-198 < y < -9.5999999999999994e-288 or 1.65e-139 < y < 6.5999999999999997e-105

   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 80.5%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-288}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-105}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+290}:\\ \;\;\;\;-y \cdot x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-110}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -7.5e+290)
     (- (* y x))
     (if (<= y -1.4e-110)
       (* y t)
       (if (<= y -6e-196)
         x
         (if (<= y 1.45e-213)
           t_1
           (if (<= y 9.5e-131) x (if (<= y 1.18e-29) t_1 (* y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -7.5e+290) {
		tmp = -(y * x);
	} else if (y <= -1.4e-110) {
		tmp = y * t;
	} else if (y <= -6e-196) {
		tmp = x;
	} else if (y <= 1.45e-213) {
		tmp = t_1;
	} else if (y <= 9.5e-131) {
		tmp = x;
	} else if (y <= 1.18e-29) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-7.5d+290)) then
        tmp = -(y * x)
    else if (y <= (-1.4d-110)) then
        tmp = y * t
    else if (y <= (-6d-196)) then
        tmp = x
    else if (y <= 1.45d-213) then
        tmp = t_1
    else if (y <= 9.5d-131) then
        tmp = x
    else if (y <= 1.18d-29) then
        tmp = t_1
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -7.5e+290) {
		tmp = -(y * x);
	} else if (y <= -1.4e-110) {
		tmp = y * t;
	} else if (y <= -6e-196) {
		tmp = x;
	} else if (y <= 1.45e-213) {
		tmp = t_1;
	} else if (y <= 9.5e-131) {
		tmp = x;
	} else if (y <= 1.18e-29) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -7.5e+290:
		tmp = -(y * x)
	elif y <= -1.4e-110:
		tmp = y * t
	elif y <= -6e-196:
		tmp = x
	elif y <= 1.45e-213:
		tmp = t_1
	elif y <= 9.5e-131:
		tmp = x
	elif y <= 1.18e-29:
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -7.5e+290)
		tmp = Float64(-Float64(y * x));
	elseif (y <= -1.4e-110)
		tmp = Float64(y * t);
	elseif (y <= -6e-196)
		tmp = x;
	elseif (y <= 1.45e-213)
		tmp = t_1;
	elseif (y <= 9.5e-131)
		tmp = x;
	elseif (y <= 1.18e-29)
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -7.5e+290)
		tmp = -(y * x);
	elseif (y <= -1.4e-110)
		tmp = y * t;
	elseif (y <= -6e-196)
		tmp = x;
	elseif (y <= 1.45e-213)
		tmp = t_1;
	elseif (y <= 9.5e-131)
		tmp = x;
	elseif (y <= 1.18e-29)
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -7.5e+290], (-N[(y * x), $MachinePrecision]), If[LessEqual[y, -1.4e-110], N[(y * t), $MachinePrecision], If[LessEqual[y, -6e-196], x, If[LessEqual[y, 1.45e-213], t$95$1, If[LessEqual[y, 9.5e-131], x, If[LessEqual[y, 1.18e-29], t$95$1, N[(y * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.50000000000000038e290

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   if -7.50000000000000038e290 < y < -1.4e-110 or 1.17999999999999996e-29 < y

   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 63.4%

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

   4. Taylor expanded in y around inf 52.3%

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

      1. *-commutative 52.3%

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

   6. Simplified 52.3%

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

   if -1.4e-110 < y < -6e-196 or 1.45e-213 < y < 9.4999999999999996e-131

   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 93.4%

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

      1. mul-1-neg 93.4%

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

      2. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in z around 0 59.1%

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

   if -6e-196 < y < 1.45e-213 or 9.4999999999999996e-131 < y < 1.17999999999999996e-29

   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 54.7%

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

   4. Taylor expanded in y around 0 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. *-commutative 52.2%

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

   6. Simplified 52.2%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+290}:\\ \;\;\;\;-y \cdot x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-110}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-149}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* y (- t x))))
   (if (<= y -1.95e-20)
     t_2
     (if (<= y -1.65e-197)
       (* x (+ z 1.0))
       (if (<= y 1.25e-213)
         t_1
         (if (<= y 3.2e-149) (+ x (* z x)) (if (<= y 3.9e+14) t_1 t_2)))))))

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 (y <= -1.95e-20) {
		tmp = t_2;
	} else if (y <= -1.65e-197) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.25e-213) {
		tmp = t_1;
	} else if (y <= 3.2e-149) {
		tmp = x + (z * x);
	} else if (y <= 3.9e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = y * (t - x)
    if (y <= (-1.95d-20)) then
        tmp = t_2
    else if (y <= (-1.65d-197)) then
        tmp = x * (z + 1.0d0)
    else if (y <= 1.25d-213) then
        tmp = t_1
    else if (y <= 3.2d-149) then
        tmp = x + (z * x)
    else if (y <= 3.9d+14) 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 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -1.95e-20) {
		tmp = t_2;
	} else if (y <= -1.65e-197) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.25e-213) {
		tmp = t_1;
	} else if (y <= 3.2e-149) {
		tmp = x + (z * x);
	} else if (y <= 3.9e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = y * (t - x)
	tmp = 0
	if y <= -1.95e-20:
		tmp = t_2
	elif y <= -1.65e-197:
		tmp = x * (z + 1.0)
	elif y <= 1.25e-213:
		tmp = t_1
	elif y <= 3.2e-149:
		tmp = x + (z * x)
	elif y <= 3.9e+14:
		tmp = t_1
	else:
		tmp = t_2
	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 (y <= -1.95e-20)
		tmp = t_2;
	elseif (y <= -1.65e-197)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 1.25e-213)
		tmp = t_1;
	elseif (y <= 3.2e-149)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 3.9e+14)
		tmp = t_1;
	else
		tmp = t_2;
	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 (y <= -1.95e-20)
		tmp = t_2;
	elseif (y <= -1.65e-197)
		tmp = x * (z + 1.0);
	elseif (y <= 1.25e-213)
		tmp = t_1;
	elseif (y <= 3.2e-149)
		tmp = x + (z * x);
	elseif (y <= 3.9e+14)
		tmp = t_1;
	else
		tmp = t_2;
	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[y, -1.95e-20], t$95$2, If[LessEqual[y, -1.65e-197], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-213], t$95$1, If[LessEqual[y, 3.2e-149], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+14], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.95000000000000004e-20 or 3.9e14 < 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 83.9%

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

   if -1.95000000000000004e-20 < y < -1.6499999999999999e-197

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 68.6%

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

      1. mul-1-neg 68.6%

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

      2. unsub-neg 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in y around 0 68.6%

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

      1. +-commutative 68.6%

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

   8. Simplified 68.6%

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

   if -1.6499999999999999e-197 < y < 1.24999999999999994e-213 or 3.20000000000000002e-149 < y < 3.9e14

   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 67.3%

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

      1. mul-1-neg 67.3%

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

      2. distribute-rgt-neg-in 67.3%

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

      3. neg-sub0 67.3%

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

      4. sub-neg 67.3%

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

      5. +-commutative 67.3%

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

      6. associate--r+ 67.3%

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

      7. neg-sub0 67.3%

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

      8. remove-double-neg 67.3%

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

   5. Simplified 67.3%

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

   if 1.24999999999999994e-213 < y < 3.20000000000000002e-149

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. unsub-neg 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in y around 0 68.4%

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

      1. +-commutative 68.4%

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

   8. Simplified 68.4%

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

      1. distribute-rgt-in 68.4%

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

      2. *-un-lft-identity 68.4%

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

   10. Applied egg-rr 68.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-149}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-199}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-152}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* y (- t x))) (t_3 (* x (+ z 1.0))))
   (if (<= y -1.5e-20)
     t_2
     (if (<= y -4e-199)
       t_3
       (if (<= y 1.4e-213)
         t_1
         (if (<= y 7.1e-152) t_3 (if (<= y 4.1e+15) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = y * (t - x);
	double t_3 = x * (z + 1.0);
	double tmp;
	if (y <= -1.5e-20) {
		tmp = t_2;
	} else if (y <= -4e-199) {
		tmp = t_3;
	} else if (y <= 1.4e-213) {
		tmp = t_1;
	} else if (y <= 7.1e-152) {
		tmp = t_3;
	} else if (y <= 4.1e+15) {
		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 = z * (x - t)
    t_2 = y * (t - x)
    t_3 = x * (z + 1.0d0)
    if (y <= (-1.5d-20)) then
        tmp = t_2
    else if (y <= (-4d-199)) then
        tmp = t_3
    else if (y <= 1.4d-213) then
        tmp = t_1
    else if (y <= 7.1d-152) then
        tmp = t_3
    else if (y <= 4.1d+15) 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 = z * (x - t);
	double t_2 = y * (t - x);
	double t_3 = x * (z + 1.0);
	double tmp;
	if (y <= -1.5e-20) {
		tmp = t_2;
	} else if (y <= -4e-199) {
		tmp = t_3;
	} else if (y <= 1.4e-213) {
		tmp = t_1;
	} else if (y <= 7.1e-152) {
		tmp = t_3;
	} else if (y <= 4.1e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = y * (t - x)
	t_3 = x * (z + 1.0)
	tmp = 0
	if y <= -1.5e-20:
		tmp = t_2
	elif y <= -4e-199:
		tmp = t_3
	elif y <= 1.4e-213:
		tmp = t_1
	elif y <= 7.1e-152:
		tmp = t_3
	elif y <= 4.1e+15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -1.5e-20)
		tmp = t_2;
	elseif (y <= -4e-199)
		tmp = t_3;
	elseif (y <= 1.4e-213)
		tmp = t_1;
	elseif (y <= 7.1e-152)
		tmp = t_3;
	elseif (y <= 4.1e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = y * (t - x);
	t_3 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -1.5e-20)
		tmp = t_2;
	elseif (y <= -4e-199)
		tmp = t_3;
	elseif (y <= 1.4e-213)
		tmp = t_1;
	elseif (y <= 7.1e-152)
		tmp = t_3;
	elseif (y <= 4.1e+15)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$3 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e-20], t$95$2, If[LessEqual[y, -4e-199], t$95$3, If[LessEqual[y, 1.4e-213], t$95$1, If[LessEqual[y, 7.1e-152], t$95$3, If[LessEqual[y, 4.1e+15], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.50000000000000014e-20 or 4.1e15 < 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 83.9%

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

   if -1.50000000000000014e-20 < y < -3.99999999999999993e-199 or 1.4e-213 < y < 7.10000000000000011e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. unsub-neg 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in y around 0 68.5%

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

      1. +-commutative 68.5%

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

   8. Simplified 68.5%

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

   if -3.99999999999999993e-199 < y < 1.4e-213 or 7.10000000000000011e-152 < y < 4.1e15

   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 67.3%

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

      1. mul-1-neg 67.3%

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

      2. distribute-rgt-neg-in 67.3%

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

      3. neg-sub0 67.3%

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

      4. sub-neg 67.3%

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

      5. +-commutative 67.3%

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

      6. associate--r+ 67.3%

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

      7. neg-sub0 67.3%

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

      8. remove-double-neg 67.3%

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

   5. Simplified 67.3%

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

Alternative 6: 37.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-112}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-194}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -3.6e-112)
     (* y t)
     (if (<= y -6.8e-194)
       x
       (if (<= y 1.8e-213)
         t_1
         (if (<= y 1.2e-131) x (if (<= y 4.4e-31) t_1 (* y t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -3.6e-112) {
		tmp = y * t;
	} else if (y <= -6.8e-194) {
		tmp = x;
	} else if (y <= 1.8e-213) {
		tmp = t_1;
	} else if (y <= 1.2e-131) {
		tmp = x;
	} else if (y <= 4.4e-31) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-3.6d-112)) then
        tmp = y * t
    else if (y <= (-6.8d-194)) then
        tmp = x
    else if (y <= 1.8d-213) then
        tmp = t_1
    else if (y <= 1.2d-131) then
        tmp = x
    else if (y <= 4.4d-31) then
        tmp = t_1
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -3.6e-112) {
		tmp = y * t;
	} else if (y <= -6.8e-194) {
		tmp = x;
	} else if (y <= 1.8e-213) {
		tmp = t_1;
	} else if (y <= 1.2e-131) {
		tmp = x;
	} else if (y <= 4.4e-31) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -3.6e-112:
		tmp = y * t
	elif y <= -6.8e-194:
		tmp = x
	elif y <= 1.8e-213:
		tmp = t_1
	elif y <= 1.2e-131:
		tmp = x
	elif y <= 4.4e-31:
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -3.6e-112)
		tmp = Float64(y * t);
	elseif (y <= -6.8e-194)
		tmp = x;
	elseif (y <= 1.8e-213)
		tmp = t_1;
	elseif (y <= 1.2e-131)
		tmp = x;
	elseif (y <= 4.4e-31)
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -3.6e-112)
		tmp = y * t;
	elseif (y <= -6.8e-194)
		tmp = x;
	elseif (y <= 1.8e-213)
		tmp = t_1;
	elseif (y <= 1.2e-131)
		tmp = x;
	elseif (y <= 4.4e-31)
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -3.6e-112], N[(y * t), $MachinePrecision], If[LessEqual[y, -6.8e-194], x, If[LessEqual[y, 1.8e-213], t$95$1, If[LessEqual[y, 1.2e-131], x, If[LessEqual[y, 4.4e-31], t$95$1, N[(y * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e-112 or 4.40000000000000019e-31 < y

   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 61.5%

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

   4. Taylor expanded in y around inf 50.7%

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

      1. *-commutative 50.7%

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

   6. Simplified 50.7%

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

   if -3.6000000000000001e-112 < y < -6.80000000000000018e-194 or 1.8e-213 < y < 1.2e-131

   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 93.4%

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

      1. mul-1-neg 93.4%

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

      2. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in z around 0 59.1%

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

   if -6.80000000000000018e-194 < y < 1.8e-213 or 1.2e-131 < y < 4.40000000000000019e-31

   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 54.7%

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

   4. Taylor expanded in y around 0 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. *-commutative 52.2%

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

   6. Simplified 52.2%

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

Alternative 7: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -850000 \lor \neg \left(t \leq -1.45 \cdot 10^{-32} \lor \neg \left(t \leq -4.8 \cdot 10^{-139}\right) \land t \leq 6.4 \cdot 10^{+35}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -850000.0)
         (not
          (or (<= t -1.45e-32) (and (not (<= t -4.8e-139)) (<= t 6.4e+35)))))
   (* (- y z) t)
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -850000.0) || !((t <= -1.45e-32) || (!(t <= -4.8e-139) && (t <= 6.4e+35)))) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-850000.0d0)) .or. (.not. (t <= (-1.45d-32)) .or. (.not. (t <= (-4.8d-139))) .and. (t <= 6.4d+35))) then
        tmp = (y - z) * t
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -850000.0) || !((t <= -1.45e-32) || (!(t <= -4.8e-139) && (t <= 6.4e+35)))) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -850000.0) or not ((t <= -1.45e-32) or (not (t <= -4.8e-139) and (t <= 6.4e+35))):
		tmp = (y - z) * t
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -850000.0) || !((t <= -1.45e-32) || (!(t <= -4.8e-139) && (t <= 6.4e+35))))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -850000.0) || ~(((t <= -1.45e-32) || (~((t <= -4.8e-139)) && (t <= 6.4e+35)))))
		tmp = (y - z) * t;
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -850000.0], N[Not[Or[LessEqual[t, -1.45e-32], And[N[Not[LessEqual[t, -4.8e-139]], $MachinePrecision], LessEqual[t, 6.4e+35]]]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5e5 or -1.44999999999999998e-32 < t < -4.80000000000000029e-139 or 6.39999999999999965e35 < t

   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 82.3%

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

   if -8.5e5 < t < -1.44999999999999998e-32 or -4.80000000000000029e-139 < t < 6.39999999999999965e35

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.2%

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

      1. mul-1-neg 80.2%

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

      2. unsub-neg 80.2%

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

   5. Simplified 80.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -850000 \lor \neg \left(t \leq -1.45 \cdot 10^{-32} \lor \neg \left(t \leq -4.8 \cdot 10^{-139}\right) \land t \leq 6.4 \cdot 10^{+35}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -3700:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-148} \lor \neg \left(t \leq 2.25 \cdot 10^{-76}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -3700.0)
     t_1
     (if (<= t -2e-33)
       (* x (- 1.0 y))
       (if (or (<= t -8.4e-148) (not (<= t 2.25e-76))) t_1 (* x (+ z 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -3700.0) {
		tmp = t_1;
	} else if (t <= -2e-33) {
		tmp = x * (1.0 - y);
	} else if ((t <= -8.4e-148) || !(t <= 2.25e-76)) {
		tmp = t_1;
	} else {
		tmp = x * (z + 1.0);
	}
	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 (t <= (-3700.0d0)) then
        tmp = t_1
    else if (t <= (-2d-33)) then
        tmp = x * (1.0d0 - y)
    else if ((t <= (-8.4d-148)) .or. (.not. (t <= 2.25d-76))) then
        tmp = t_1
    else
        tmp = x * (z + 1.0d0)
    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 (t <= -3700.0) {
		tmp = t_1;
	} else if (t <= -2e-33) {
		tmp = x * (1.0 - y);
	} else if ((t <= -8.4e-148) || !(t <= 2.25e-76)) {
		tmp = t_1;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -3700.0:
		tmp = t_1
	elif t <= -2e-33:
		tmp = x * (1.0 - y)
	elif (t <= -8.4e-148) or not (t <= 2.25e-76):
		tmp = t_1
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -3700.0)
		tmp = t_1;
	elseif (t <= -2e-33)
		tmp = Float64(x * Float64(1.0 - y));
	elseif ((t <= -8.4e-148) || !(t <= 2.25e-76))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -3700.0)
		tmp = t_1;
	elseif (t <= -2e-33)
		tmp = x * (1.0 - y);
	elseif ((t <= -8.4e-148) || ~((t <= 2.25e-76)))
		tmp = t_1;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -3700.0], t$95$1, If[LessEqual[t, -2e-33], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -8.4e-148], N[Not[LessEqual[t, 2.25e-76]], $MachinePrecision]], t$95$1, N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3700 or -2.0000000000000001e-33 < t < -8.4000000000000001e-148 or 2.25e-76 < t

   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 76.8%

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

   if -3700 < t < -2.0000000000000001e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 72.5%

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

   if -8.4000000000000001e-148 < t < 2.25e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in y around 0 63.8%

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

      1. +-commutative 63.8%

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

   8. Simplified 63.8%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3700:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-148} \lor \neg \left(t \leq 2.25 \cdot 10^{-76}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-306}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-213}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e-119)
   (* y t)
   (if (<= y -2.1e-306)
     x
     (if (<= y 1.9e-213) (* z x) (if (<= y 4.7e-29) x (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e-119) {
		tmp = y * t;
	} else if (y <= -2.1e-306) {
		tmp = x;
	} else if (y <= 1.9e-213) {
		tmp = z * x;
	} else if (y <= 4.7e-29) {
		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 <= (-4.2d-119)) then
        tmp = y * t
    else if (y <= (-2.1d-306)) then
        tmp = x
    else if (y <= 1.9d-213) then
        tmp = z * x
    else if (y <= 4.7d-29) 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 <= -4.2e-119) {
		tmp = y * t;
	} else if (y <= -2.1e-306) {
		tmp = x;
	} else if (y <= 1.9e-213) {
		tmp = z * x;
	} else if (y <= 4.7e-29) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e-119:
		tmp = y * t
	elif y <= -2.1e-306:
		tmp = x
	elif y <= 1.9e-213:
		tmp = z * x
	elif y <= 4.7e-29:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e-119)
		tmp = Float64(y * t);
	elseif (y <= -2.1e-306)
		tmp = x;
	elseif (y <= 1.9e-213)
		tmp = Float64(z * x);
	elseif (y <= 4.7e-29)
		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 <= -4.2e-119)
		tmp = y * t;
	elseif (y <= -2.1e-306)
		tmp = x;
	elseif (y <= 1.9e-213)
		tmp = z * x;
	elseif (y <= 4.7e-29)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e-119], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.1e-306], x, If[LessEqual[y, 1.9e-213], N[(z * x), $MachinePrecision], If[LessEqual[y, 4.7e-29], x, N[(y * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e-119 or 4.6999999999999998e-29 < y

   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 61.8%

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

   4. Taylor expanded in y around inf 51.0%

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

      1. *-commutative 51.0%

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

   6. Simplified 51.0%

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

   if -4.2e-119 < y < -2.1000000000000001e-306 or 1.9e-213 < y < 4.6999999999999998e-29

   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 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in z around 0 45.4%

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

   if -2.1000000000000001e-306 < y < 1.9e-213

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-rgt-neg-in 80.3%

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

      3. neg-sub0 80.3%

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

      4. sub-neg 80.3%

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

      5. +-commutative 80.3%

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

      6. associate--r+ 80.3%

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

      7. neg-sub0 80.3%

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

      8. remove-double-neg 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in x around inf 42.5%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-306}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-213}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-105}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -7.8e-42)
     t_1
     (if (<= y 5.8e-105)
       (- x (* z t))
       (if (<= y 1.65e+14) (* x (+ z 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -7.8e-42) {
		tmp = t_1;
	} else if (y <= 5.8e-105) {
		tmp = x - (z * t);
	} else if (y <= 1.65e+14) {
		tmp = x * (z + 1.0);
	} 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 <= (-7.8d-42)) then
        tmp = t_1
    else if (y <= 5.8d-105) then
        tmp = x - (z * t)
    else if (y <= 1.65d+14) then
        tmp = x * (z + 1.0d0)
    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 <= -7.8e-42) {
		tmp = t_1;
	} else if (y <= 5.8e-105) {
		tmp = x - (z * t);
	} else if (y <= 1.65e+14) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -7.8e-42:
		tmp = t_1
	elif y <= 5.8e-105:
		tmp = x - (z * t)
	elif y <= 1.65e+14:
		tmp = x * (z + 1.0)
	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 <= -7.8e-42)
		tmp = t_1;
	elseif (y <= 5.8e-105)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 1.65e+14)
		tmp = Float64(x * Float64(z + 1.0));
	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 <= -7.8e-42)
		tmp = t_1;
	elseif (y <= 5.8e-105)
		tmp = x - (z * t);
	elseif (y <= 1.65e+14)
		tmp = x * (z + 1.0);
	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, -7.8e-42], t$95$1, If[LessEqual[y, 5.8e-105], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+14], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.8000000000000003e-42 or 1.65e14 < 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 81.8%

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

   if -7.8000000000000003e-42 < y < 5.80000000000000007e-105

   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 92.8%

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

      1. mul-1-neg 92.8%

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

      2. unsub-neg 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in t around inf 74.1%

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

      1. *-commutative 74.1%

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

   8. Simplified 74.1%

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

   if 5.80000000000000007e-105 < y < 1.65e14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in y around 0 64.6%

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

      1. +-commutative 64.6%

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

   8. Simplified 64.6%

      \[\leadsto \color{blue}{x \cdot \left(z + 1\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 54.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-67} \lor \neg \left(y - z \leq 4 \cdot 10^{-62}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (- y z) -5e-67) (not (<= (- y z) 4e-62))) (* (- y z) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -5e-67) || !((y - z) <= 4e-62)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((y - z) <= (-5d-67)) .or. (.not. ((y - z) <= 4d-62))) then
        tmp = (y - z) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -5e-67) || !((y - z) <= 4e-62)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y - z) <= -5e-67) or not ((y - z) <= 4e-62):
		tmp = (y - z) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y - z) <= -5e-67) || !(Float64(y - z) <= 4e-62))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y - z) <= -5e-67) || ~(((y - z) <= 4e-62)))
		tmp = (y - z) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y - z), $MachinePrecision], -5e-67], N[Not[LessEqual[N[(y - z), $MachinePrecision], 4e-62]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -4.9999999999999999e-67 or 4.0000000000000002e-62 < (-.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 60.2%

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

   if -4.9999999999999999e-67 < (-.f64 y z) < 4.0000000000000002e-62

   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 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in z around 0 74.0%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-67} \lor \neg \left(y - z \leq 4 \cdot 10^{-62}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-20} \lor \neg \left(y \leq 1.92 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.95e-20) (not (<= y 1.92e+15)))
   (* y (- t x))
   (- x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.95e-20) || !(y <= 1.92e+15)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * (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 ((y <= (-1.95d-20)) .or. (.not. (y <= 1.92d+15))) then
        tmp = y * (t - x)
    else
        tmp = x - (z * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.95e-20) || !(y <= 1.92e+15)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.95e-20) or not (y <= 1.92e+15):
		tmp = y * (t - x)
	else:
		tmp = x - (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.95e-20) || !(y <= 1.92e+15))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x - Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.95e-20) || ~((y <= 1.92e+15)))
		tmp = y * (t - x);
	else
		tmp = x - (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.95e-20], N[Not[LessEqual[y, 1.92e+15]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95000000000000004e-20 or 1.92e15 < 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 83.9%

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

   if -1.95000000000000004e-20 < y < 1.92e15

   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 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-20} \lor \neg \left(y \leq 1.92 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-148} \lor \neg \left(t \leq 9.5 \cdot 10^{-78}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.4e-148) (not (<= t 9.5e-78))) (* (- y z) t) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.4e-148) || !(t <= 9.5e-78)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-8.4d-148)) .or. (.not. (t <= 9.5d-78))) then
        tmp = (y - z) * t
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.4e-148) || !(t <= 9.5e-78)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.4e-148) or not (t <= 9.5e-78):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.4e-148) || !(t <= 9.5e-78))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.4e-148) || ~((t <= 9.5e-78)))
		tmp = (y - z) * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.4e-148], N[Not[LessEqual[t, 9.5e-78]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.4000000000000001e-148 or 9.4999999999999997e-78 < t

   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 73.7%

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

   if -8.4000000000000001e-148 < t < 9.4999999999999997e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in y around 0 63.8%

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

      1. +-commutative 63.8%

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

   8. Simplified 63.8%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-148} \lor \neg \left(t \leq 9.5 \cdot 10^{-78}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.26 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.26e-14))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.26e-14)) {
		tmp = z * 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 ((z <= (-1.0d0)) .or. (.not. (z <= 1.26d-14))) then
        tmp = z * 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 ((z <= -1.0) || !(z <= 1.26e-14)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.26e-14):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.26e-14))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.26e-14)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.26e-14]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.25999999999999996e-14 < z

   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 73.0%

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

      1. mul-1-neg 73.0%

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

      2. distribute-rgt-neg-in 73.0%

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

      3. neg-sub0 73.0%

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

      4. sub-neg 73.0%

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

      5. +-commutative 73.0%

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

      6. associate--r+ 73.0%

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

      7. neg-sub0 73.0%

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

      8. remove-double-neg 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in x around inf 39.8%

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

   if -1 < z < 1.25999999999999996e-14

   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 41.5%

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

      1. mul-1-neg 41.5%

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

      2. unsub-neg 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in z around 0 31.4%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.26 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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 16: 17.9% 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 0 56.5%

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

   1. mul-1-neg 56.5%

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

   2. unsub-neg 56.5%

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

5. Simplified 56.5%

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

6. Taylor expanded in z around 0 18.3%

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

Developer target: 96.3% 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 2024086 
(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))))