Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.0% → 97.0%

Time: 7.9s

Alternatives: 16

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.9%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 92.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+18} \lor \neg \left(z \leq 7.5 \cdot 10^{+97}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot a}{1 + \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+18) (not (<= z 7.5e+97)))
   (fma (/ z (- (+ 1.0 t) z)) a x)
   (- x (/ (* (- y z) a) (+ 1.0 (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+18) || !(z <= 7.5e+97)) {
		tmp = fma((z / ((1.0 + t) - z)), a, x);
	} else {
		tmp = x - (((y - z) * a) / (1.0 + (t - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+18) || !(z <= 7.5e+97))
		tmp = fma(Float64(z / Float64(Float64(1.0 + t) - z)), a, x);
	else
		tmp = Float64(x - Float64(Float64(Float64(y - z) * a) / Float64(1.0 + Float64(t - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+18], N[Not[LessEqual[z, 7.5e+97]], $MachinePrecision]], N[(N[(z / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], N[(x - N[(N[(N[(y - z), $MachinePrecision] * a), $MachinePrecision] / N[(1.0 + N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e18 or 7.5000000000000004e97 < z

   1. Initial program 95.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 90.6

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 90.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

   if -1.6e18 < z < 7.5000000000000004e97

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 94.8

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 94.8

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

   4. Applied rewrites 94.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+18} \lor \neg \left(z \leq 7.5 \cdot 10^{+97}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot a}{1 + \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 + t\right) - z\\ \mathbf{if}\;z \leq -2 \cdot 10^{+14} \lor \neg \left(z \leq 3.2 \cdot 10^{+98}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t\_1}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t\_1} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ 1.0 t) z)))
   (if (or (<= z -2e+14) (not (<= z 3.2e+98)))
     (fma (/ z t_1) a x)
     (- x (* (/ y t_1) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 + t) - z;
	double tmp;
	if ((z <= -2e+14) || !(z <= 3.2e+98)) {
		tmp = fma((z / t_1), a, x);
	} else {
		tmp = x - ((y / t_1) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(1.0 + t) - z)
	tmp = 0.0
	if ((z <= -2e+14) || !(z <= 3.2e+98))
		tmp = fma(Float64(z / t_1), a, x);
	else
		tmp = Float64(x - Float64(Float64(y / t_1) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]}, If[Or[LessEqual[z, -2e+14], N[Not[LessEqual[z, 3.2e+98]], $MachinePrecision]], N[(N[(z / t$95$1), $MachinePrecision] * a + x), $MachinePrecision], N[(x - N[(N[(y / t$95$1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2e14 or 3.2000000000000002e98 < z

   1. Initial program 95.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 91.6

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

   if -2e14 < z < 3.2000000000000002e98

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 90.7

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

   5. Applied rewrites 90.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+14} \lor \neg \left(z \leq 3.2 \cdot 10^{+98}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\left(1 + t\right) - z} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{t}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+73}:\\ \;\;\;\;x - a \cdot t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+124}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t\_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) t)))
   (if (<= t -5.6e+73)
     (- x (* a t_1))
     (if (<= t 1.95e+124)
       (- x (* (- y z) (/ a (- 1.0 z))))
       (fma (- a) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / t;
	double tmp;
	if (t <= -5.6e+73) {
		tmp = x - (a * t_1);
	} else if (t <= 1.95e+124) {
		tmp = x - ((y - z) * (a / (1.0 - z)));
	} else {
		tmp = fma(-a, t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / t)
	tmp = 0.0
	if (t <= -5.6e+73)
		tmp = Float64(x - Float64(a * t_1));
	elseif (t <= 1.95e+124)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / Float64(1.0 - z))));
	else
		tmp = fma(Float64(-a), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -5.6e+73], N[(x - N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+124], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * t$95$1 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.60000000000000016e73

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

   7. Applied rewrites 89.7%

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

   if -5.60000000000000016e73 < t < 1.95e124

   1. Initial program 96.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 90.8

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

   5. Applied rewrites 90.8%

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

   if 1.95e124 < t

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 76.3

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 76.3

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

   4. Applied rewrites 76.3%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. mul-1-neg N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 88.7

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

   7. Applied rewrites 88.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 87.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+14} \lor \neg \left(z \leq 1.1 \cdot 10^{+81}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.32e+14) (not (<= z 1.1e+81)))
   (fma (/ z (- (+ 1.0 t) z)) a x)
   (- x (* (/ y (+ 1.0 t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.32e+14) || !(z <= 1.1e+81)) {
		tmp = fma((z / ((1.0 + t) - z)), a, x);
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.32e+14) || !(z <= 1.1e+81))
		tmp = fma(Float64(z / Float64(Float64(1.0 + t) - z)), a, x);
	else
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.32e+14], N[Not[LessEqual[z, 1.1e+81]], $MachinePrecision]], N[(N[(z / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32e14 or 1.09999999999999993e81 < z

   1. Initial program 95.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 88.8

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 88.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

   if -1.32e14 < z < 1.09999999999999993e81

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 90.1

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

   5. Applied rewrites 90.1%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+14} \lor \neg \left(z \leq 1.1 \cdot 10^{+81}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+14} \lor \neg \left(z \leq 1.1 \cdot 10^{+81}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{\left(t + 1\right) - z}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.32e+14) (not (<= z 1.1e+81)))
   (fma (/ a (- (+ t 1.0) z)) z x)
   (- x (* (/ y (+ 1.0 t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.32e+14) || !(z <= 1.1e+81)) {
		tmp = fma((a / ((t + 1.0) - z)), z, x);
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.32e+14) || !(z <= 1.1e+81))
		tmp = fma(Float64(a / Float64(Float64(t + 1.0) - z)), z, x);
	else
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.32e+14], N[Not[LessEqual[z, 1.1e+81]], $MachinePrecision]], N[(N[(a / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32e14 or 1.09999999999999993e81 < z

   1. Initial program 95.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 88.8

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 88.8%

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

   7. Applied rewrites 86.4%

      \[\leadsto \mathsf{fma}\left(\frac{a}{\left(t + 1\right) - z}, \color{blue}{z}, x\right) \]

   if -1.32e14 < z < 1.09999999999999993e81

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 90.1

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

   5. Applied rewrites 90.1%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+14} \lor \neg \left(z \leq 1.1 \cdot 10^{+81}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{\left(t + 1\right) - z}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{t}, z, x\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-26}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.75e+18)
   (- x a)
   (if (<= z -1.28e-34)
     (fma (/ a t) z x)
     (if (<= z 1.12e-26) (- x (* (- y z) (fma a z a))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.75e+18) {
		tmp = x - a;
	} else if (z <= -1.28e-34) {
		tmp = fma((a / t), z, x);
	} else if (z <= 1.12e-26) {
		tmp = x - ((y - z) * fma(a, z, a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.75e+18)
		tmp = Float64(x - a);
	elseif (z <= -1.28e-34)
		tmp = fma(Float64(a / t), z, x);
	elseif (z <= 1.12e-26)
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.75e+18], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.28e-34], N[(N[(a / t), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[z, 1.12e-26], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.75e18 or 1.12e-26 < z

   1. Initial program 96.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 75.2

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

   5. Applied rewrites 75.2%

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

   if -2.75e18 < z < -1.2799999999999999e-34

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 91.1

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 91.1%

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

   7. Applied rewrites 91.1%

      \[\leadsto \mathsf{fma}\left(\frac{a}{\left(t + 1\right) - z}, \color{blue}{z}, x\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\frac{a}{t}, z, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 91.1%

       \[\leadsto \mathsf{fma}\left(\frac{a}{t}, z, x\right) \]

   if -1.2799999999999999e-34 < z < 1.12e-26

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 68.4

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

   5. Applied rewrites 68.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 68.4%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-34}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{t}, z, x\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-26}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+17} \lor \neg \left(z \leq 1.7 \cdot 10^{+81}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e+17) (not (<= z 1.7e+81)))
   (- x a)
   (- x (* (/ y (+ 1.0 t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e+17) || !(z <= 1.7e+81)) {
		tmp = x - a;
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5d+17)) .or. (.not. (z <= 1.7d+81))) then
        tmp = x - a
    else
        tmp = x - ((y / (1.0d0 + t)) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e+17) || !(z <= 1.7e+81)) {
		tmp = x - a;
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5e+17) or not (z <= 1.7e+81):
		tmp = x - a
	else:
		tmp = x - ((y / (1.0 + t)) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e+17) || !(z <= 1.7e+81))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5e+17) || ~((z <= 1.7e+81)))
		tmp = x - a;
	else
		tmp = x - ((y / (1.0 + t)) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e+17], N[Not[LessEqual[z, 1.7e+81]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e17 or 1.70000000000000001e81 < z

   1. Initial program 95.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 77.7

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

   5. Applied rewrites 77.7%

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

   if -5e17 < z < 1.70000000000000001e81

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 88.9

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

   5. Applied rewrites 88.9%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+17} \lor \neg \left(z \leq 1.7 \cdot 10^{+81}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+73} \lor \neg \left(t \leq 3 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e+73) (not (<= t 3e+18)))
   (fma (- a) (/ (- y z) t) x)
   (- x (* a (/ y (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+73) || !(t <= 3e+18)) {
		tmp = fma(-a, ((y - z) / t), x);
	} else {
		tmp = x - (a * (y / (1.0 - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e+73) || !(t <= 3e+18))
		tmp = fma(Float64(-a), Float64(Float64(y - z) / t), x);
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e+73], N[Not[LessEqual[t, 3e+18]], $MachinePrecision]], N[((-a) * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.80000000000000004e73 or 3e18 < t

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 78.8

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 78.8

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

   4. Applied rewrites 78.8%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. mul-1-neg N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 82.7

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

   7. Applied rewrites 82.7%

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

   if -4.80000000000000004e73 < t < 3e18

   1. Initial program 96.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 93.3

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

   5. Applied rewrites 93.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 73.5%

      \[\leadsto x - a \cdot \color{blue}{\frac{y}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+73} \lor \neg \left(t \leq 3 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+43} \lor \neg \left(t \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{1 - z}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.2e+43) (not (<= t 6.5e+18)))
   (fma (- a) (/ (- y z) t) x)
   (fma (/ z (- 1.0 z)) a x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+43) || !(t <= 6.5e+18)) {
		tmp = fma(-a, ((y - z) / t), x);
	} else {
		tmp = fma((z / (1.0 - z)), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.2e+43) || !(t <= 6.5e+18))
		tmp = fma(Float64(-a), Float64(Float64(y - z) / t), x);
	else
		tmp = fma(Float64(z / Float64(1.0 - z)), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.2e+43], N[Not[LessEqual[t, 6.5e+18]], $MachinePrecision]], N[((-a) * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], N[(N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2000000000000003e43 or 6.5e18 < t

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 79.0

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 79.0

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

   4. Applied rewrites 79.0%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. mul-1-neg N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 81.3

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

   7. Applied rewrites 81.3%

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

   if -6.2000000000000003e43 < t < 6.5e18

   1. Initial program 96.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 72.0

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 72.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\frac{z}{1 - z}, a, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 72.0%

      \[\leadsto \mathsf{fma}\left(\frac{z}{1 - z}, a, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+43} \lor \neg \left(t \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{1 - z}, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{t}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+73}:\\ \;\;\;\;x - a \cdot t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+18}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, t\_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) t)))
   (if (<= t -4.8e+73)
     (- x (* a t_1))
     (if (<= t 3e+18) (- x (* a (/ y (- 1.0 z)))) (fma (- a) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / t;
	double tmp;
	if (t <= -4.8e+73) {
		tmp = x - (a * t_1);
	} else if (t <= 3e+18) {
		tmp = x - (a * (y / (1.0 - z)));
	} else {
		tmp = fma(-a, t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / t)
	tmp = 0.0
	if (t <= -4.8e+73)
		tmp = Float64(x - Float64(a * t_1));
	elseif (t <= 3e+18)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))));
	else
		tmp = fma(Float64(-a), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -4.8e+73], N[(x - N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+18], N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * t$95$1 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.80000000000000004e73

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

   7. Applied rewrites 89.7%

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

   if -4.80000000000000004e73 < t < 3e18

   1. Initial program 96.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 93.3

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

   5. Applied rewrites 93.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 73.5%

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

   if 3e18 < t

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 75.6

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 75.6

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

   4. Applied rewrites 75.6%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. mul-1-neg N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 77.2

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

   7. Applied rewrites 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 65.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+18} \lor \neg \left(z \leq 2.3 \cdot 10^{-25}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{t}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e+18) (not (<= z 2.3e-25))) (- x a) (fma (/ a t) z x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e+18) || !(z <= 2.3e-25)) {
		tmp = x - a;
	} else {
		tmp = fma((a / t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.75e+18) || !(z <= 2.3e-25))
		tmp = Float64(x - a);
	else
		tmp = fma(Float64(a / t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.75e+18], N[Not[LessEqual[z, 2.3e-25]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(N[(a / t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75e18 or 2.2999999999999999e-25 < z

   1. Initial program 96.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 75.8

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

   5. Applied rewrites 75.8%

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

   if -2.75e18 < z < 2.2999999999999999e-25

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 61.3

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 61.3%

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

   7. Applied rewrites 62.2%

      \[\leadsto \mathsf{fma}\left(\frac{a}{\left(t + 1\right) - z}, \color{blue}{z}, x\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\frac{a}{t}, z, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 58.4%

       \[\leadsto \mathsf{fma}\left(\frac{a}{t}, z, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+18} \lor \neg \left(z \leq 2.3 \cdot 10^{-25}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{t}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-41} \lor \neg \left(z \leq 2.05 \cdot 10^{-25}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-41) (not (<= z 2.05e-25)))
   (- x a)
   (- x (* (fma (- y) t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-41) || !(z <= 2.05e-25)) {
		tmp = x - a;
	} else {
		tmp = x - (fma(-y, t, y) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-41) || !(z <= 2.05e-25))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(fma(Float64(-y), t, y) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-41], N[Not[LessEqual[z, 2.05e-25]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(N[((-y) * t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e-41 or 2.04999999999999994e-25 < z

   1. Initial program 96.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   if -2.7e-41 < z < 2.04999999999999994e-25

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 90.2

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

   5. Applied rewrites 90.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto x - \left(y + -1 \cdot \left(t \cdot y\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 55.2%

      \[\leadsto x - \mathsf{fma}\left(-y, t, y\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-41} \lor \neg \left(z \leq 2.05 \cdot 10^{-25}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+14} \lor \neg \left(z \leq 6.2 \cdot 10^{-54}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.6e+14) (not (<= z 6.2e-54))) (- x a) (* 1.0 x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.6e+14) || !(z <= 6.2e-54)) {
		tmp = x - a;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.6d+14)) .or. (.not. (z <= 6.2d-54))) then
        tmp = x - a
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.6e+14) || !(z <= 6.2e-54)) {
		tmp = x - a;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.6e+14) or not (z <= 6.2e-54):
		tmp = x - a
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.6e+14) || !(z <= 6.2e-54))
		tmp = Float64(x - a);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.6e+14) || ~((z <= 6.2e-54)))
		tmp = x - a;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.6e+14], N[Not[LessEqual[z, 6.2e-54]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6e14 or 6.20000000000000008e-54 < z

   1. Initial program 96.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 73.7

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

   5. Applied rewrites 73.7%

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

   if -5.6e14 < z < 6.20000000000000008e-54

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 40.2

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

   5. Applied rewrites 40.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 40.9%

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

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 53.4%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+14} \lor \neg \left(z \leq 6.2 \cdot 10^{-54}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.5% accurate, 8.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - a), $MachinePrecision]

Derivation

1. Initial program 97.9%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

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

   1. lower--.f64 58.3

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

5. Applied rewrites 58.3%

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

6. Final simplification 58.3%

   \[\leadsto x - a \]
7. Add Preprocessing

Alternative 16: 16.4% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ -a \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := (-a)

Derivation

1. Initial program 97.9%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

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

   1. lower--.f64 58.3

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

5. Applied rewrites 58.3%

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

6. Taylor expanded in x around 0

   \[\leadsto -1 \cdot \color{blue}{a} \]
7. Step-by-step derivation

8. Applied rewrites 17.8%

   \[\leadsto -a \]

9. Final simplification 17.8%

   \[\leadsto -a \]
10. Add Preprocessing

Developer Target 1: 99.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - (((y - z) / ((t - z) + 1.0d0)) * a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024320 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))