Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.0% → 97.0%

Time: 5.4s

Alternatives: 27

Speedup: 1.0×

• 36.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (- (+ t y) 2.0) b (- (fma (- 1.0 y) z x) (* (- t 1.0) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma(((t + y) - 2.0), b, (fma((1.0 - y), z, x) - ((t - 1.0) * a)));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(Float64(t + y) - 2.0), b, Float64(fma(Float64(1.0 - y), z, x) - Float64(Float64(t - 1.0) * a)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.0%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

   2. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   3. lift--.f64 N/A

      \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. lift--.f64 N/A

      \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. lift-*.f64 N/A

      \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   7. lift--.f64 N/A

      \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   9. lift-+.f64 N/A

      \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   10. lift--.f64 N/A

       \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

   11. +-commutative N/A

       \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   12. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   13. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   15. lower-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

   17. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

3. Applied rewrites 97.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]
4. Add Preprocessing

Alternative 2: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 1\right) \cdot z\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;a + \left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - t\_1\right)\\ \mathbf{elif}\;t \leq 2.3:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) - \left(t\_1 - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(-z, y, x\right) - \left(-z\right)\right) - \left(t - 1\right) \cdot a\right) + b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 1.0) z)))
   (if (<= t -2.7e+77)
     (+ a (- (fma (- y 2.0) b (* (- b a) t)) t_1))
     (if (<= t 2.3)
       (- (fma (- y 2.0) b x) (- t_1 a))
       (+ (- (- (fma (- z) y x) (- z)) (* (- t 1.0) a)) (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 1.0) * z;
	double tmp;
	if (t <= -2.7e+77) {
		tmp = a + (fma((y - 2.0), b, ((b - a) * t)) - t_1);
	} else if (t <= 2.3) {
		tmp = fma((y - 2.0), b, x) - (t_1 - a);
	} else {
		tmp = ((fma(-z, y, x) - -z) - ((t - 1.0) * a)) + (b * t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 1.0) * z)
	tmp = 0.0
	if (t <= -2.7e+77)
		tmp = Float64(a + Float64(fma(Float64(y - 2.0), b, Float64(Float64(b - a) * t)) - t_1));
	elseif (t <= 2.3)
		tmp = Float64(fma(Float64(y - 2.0), b, x) - Float64(t_1 - a));
	else
		tmp = Float64(Float64(Float64(fma(Float64(-z), y, x) - Float64(-z)) - Float64(Float64(t - 1.0) * a)) + Float64(b * t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t, -2.7e+77], N[(a + N[(N[(N[(y - 2.0), $MachinePrecision] * b + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(t$95$1 - a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[((-z) * y + x), $MachinePrecision] - (-z)), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6999999999999998e77

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   if -2.6999999999999998e77 < t < 2.2999999999999998

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

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

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      5. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   7. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)} \]

   if 2.2999999999999998 < t

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 77.6

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

   4. Applied rewrites 77.6%

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

   5. Taylor expanded in y around 0

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

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

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

      2. sub-negate-rev N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

          \[\leadsto \left(\left(\left(\left(-1 \cdot z\right) \cdot y + x\right) - -1 \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot t \]

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{fma}\left(\mathsf{neg}\left(z\right), y, x\right) - -1 \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot t \]

      14. lower-neg.f64 N/A

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

      15. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{fma}\left(-z, y, x\right) - \left(\mathsf{neg}\left(z\right)\right)\right) - \left(t - 1\right) \cdot a\right) + b \cdot t \]

      16. lower-neg.f64 77.6

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

   7. Applied rewrites 77.6%

      \[\leadsto \left(\color{blue}{\left(\mathsf{fma}\left(-z, y, x\right) - \left(-z\right)\right)} - \left(t - 1\right) \cdot a\right) + b \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 1\right) \cdot z\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;a + \left(\mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) - t\_1\right)\\ \mathbf{elif}\;t \leq 2.3:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) - \left(t\_1 - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(-z, y, x\right) - \left(-z\right)\right) - \left(t - 1\right) \cdot a\right) + b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 1.0) z)))
   (if (<= t -2.7e+77)
     (+ a (- (fma -2.0 b (* (- b a) t)) t_1))
     (if (<= t 2.3)
       (- (fma (- y 2.0) b x) (- t_1 a))
       (+ (- (- (fma (- z) y x) (- z)) (* (- t 1.0) a)) (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 1.0) * z;
	double tmp;
	if (t <= -2.7e+77) {
		tmp = a + (fma(-2.0, b, ((b - a) * t)) - t_1);
	} else if (t <= 2.3) {
		tmp = fma((y - 2.0), b, x) - (t_1 - a);
	} else {
		tmp = ((fma(-z, y, x) - -z) - ((t - 1.0) * a)) + (b * t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 1.0) * z)
	tmp = 0.0
	if (t <= -2.7e+77)
		tmp = Float64(a + Float64(fma(-2.0, b, Float64(Float64(b - a) * t)) - t_1));
	elseif (t <= 2.3)
		tmp = Float64(fma(Float64(y - 2.0), b, x) - Float64(t_1 - a));
	else
		tmp = Float64(Float64(Float64(fma(Float64(-z), y, x) - Float64(-z)) - Float64(Float64(t - 1.0) * a)) + Float64(b * t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t, -2.7e+77], N[(a + N[(N[(-2.0 * b + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(t$95$1 - a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[((-z) * y + x), $MachinePrecision] - (-z)), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6999999999999998e77

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto a + \left(\mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 71.3%

       \[\leadsto a + \left(\mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right) \]

   if -2.6999999999999998e77 < t < 2.2999999999999998

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

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

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      5. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   7. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)} \]

   if 2.2999999999999998 < t

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 77.6

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

   4. Applied rewrites 77.6%

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

   5. Taylor expanded in y around 0

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

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

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

      2. sub-negate-rev N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. mul-1-neg N/A

          \[\leadsto \left(\left(\left(\left(-1 \cdot z\right) \cdot y + x\right) - -1 \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot t \]

      12. lower-fma.f64 N/A

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

      13. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{fma}\left(\mathsf{neg}\left(z\right), y, x\right) - -1 \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot t \]

      14. lower-neg.f64 N/A

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

      15. mul-1-neg N/A

          \[\leadsto \left(\left(\mathsf{fma}\left(-z, y, x\right) - \left(\mathsf{neg}\left(z\right)\right)\right) - \left(t - 1\right) \cdot a\right) + b \cdot t \]

      16. lower-neg.f64 77.6

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

   7. Applied rewrites 77.6%

      \[\leadsto \left(\color{blue}{\left(\mathsf{fma}\left(-z, y, x\right) - \left(-z\right)\right)} - \left(t - 1\right) \cdot a\right) + b \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 1\right) \cdot z\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;a + \left(\mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) - t\_1\right)\\ \mathbf{elif}\;t \leq 2.3:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) - \left(t\_1 - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(\left(t - 1\right) \cdot a - b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 1.0) z)))
   (if (<= t -2.7e+77)
     (+ a (- (fma -2.0 b (* (- b a) t)) t_1))
     (if (<= t 2.3)
       (- (fma (- y 2.0) b x) (- t_1 a))
       (- (fma (- 1.0 y) z x) (- (* (- t 1.0) a) (* b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 1.0) * z;
	double tmp;
	if (t <= -2.7e+77) {
		tmp = a + (fma(-2.0, b, ((b - a) * t)) - t_1);
	} else if (t <= 2.3) {
		tmp = fma((y - 2.0), b, x) - (t_1 - a);
	} else {
		tmp = fma((1.0 - y), z, x) - (((t - 1.0) * a) - (b * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 1.0) * z)
	tmp = 0.0
	if (t <= -2.7e+77)
		tmp = Float64(a + Float64(fma(-2.0, b, Float64(Float64(b - a) * t)) - t_1));
	elseif (t <= 2.3)
		tmp = Float64(fma(Float64(y - 2.0), b, x) - Float64(t_1 - a));
	else
		tmp = Float64(fma(Float64(1.0 - y), z, x) - Float64(Float64(Float64(t - 1.0) * a) - Float64(b * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t, -2.7e+77], N[(a + N[(N[(-2.0 * b + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(t$95$1 - a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] - N[(N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision] - N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6999999999999998e77

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto a + \left(\mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 71.3%

       \[\leadsto a + \left(\mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right) \]

   if -2.6999999999999998e77 < t < 2.2999999999999998

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

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

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      5. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   7. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)} \]

   if 2.2999999999999998 < t

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 77.6

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

   4. Applied rewrites 77.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. associate-+l- N/A

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

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

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

      10. sub-negate-rev N/A

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

      11. *-commutative N/A

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

      12. lower--.f64 N/A

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

   6. Applied rewrites 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x\right) - \left(\left(t - 1\right) \cdot a - b \cdot t\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 1\right) \cdot z\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;\left(\left(x - t\_1\right) - a \cdot t\right) + b \cdot t\\ \mathbf{elif}\;t \leq 2.3:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) - \left(t\_1 - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) - \left(\left(t - 1\right) \cdot a - b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 1.0) z)))
   (if (<= t -2.7e+77)
     (+ (- (- x t_1) (* a t)) (* b t))
     (if (<= t 2.3)
       (- (fma (- y 2.0) b x) (- t_1 a))
       (- (fma (- 1.0 y) z x) (- (* (- t 1.0) a) (* b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 1.0) * z;
	double tmp;
	if (t <= -2.7e+77) {
		tmp = ((x - t_1) - (a * t)) + (b * t);
	} else if (t <= 2.3) {
		tmp = fma((y - 2.0), b, x) - (t_1 - a);
	} else {
		tmp = fma((1.0 - y), z, x) - (((t - 1.0) * a) - (b * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 1.0) * z)
	tmp = 0.0
	if (t <= -2.7e+77)
		tmp = Float64(Float64(Float64(x - t_1) - Float64(a * t)) + Float64(b * t));
	elseif (t <= 2.3)
		tmp = Float64(fma(Float64(y - 2.0), b, x) - Float64(t_1 - a));
	else
		tmp = Float64(fma(Float64(1.0 - y), z, x) - Float64(Float64(Float64(t - 1.0) * a) - Float64(b * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t, -2.7e+77], N[(N[(N[(x - t$95$1), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(t$95$1 - a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] - N[(N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision] - N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6999999999999998e77

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 77.6

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

   4. Applied rewrites 77.6%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 68.6

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

   7. Applied rewrites 68.6%

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

   if -2.6999999999999998e77 < t < 2.2999999999999998

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

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

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      5. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   7. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)} \]

   if 2.2999999999999998 < t

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 77.6

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

   4. Applied rewrites 77.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. associate-+l- N/A

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

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

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

      10. sub-negate-rev N/A

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

      11. *-commutative N/A

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

      12. lower--.f64 N/A

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

   6. Applied rewrites 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x\right) - \left(\left(t - 1\right) \cdot a - b \cdot t\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 1\right) \cdot z\\ t_2 := \left(\left(x - t\_1\right) - a \cdot t\right) + b \cdot t\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.2:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) - \left(t\_1 - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 1.0) z)) (t_2 (+ (- (- x t_1) (* a t)) (* b t))))
   (if (<= t -2.7e+77)
     t_2
     (if (<= t 3.2) (- (fma (- y 2.0) b x) (- t_1 a)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 1.0) * z;
	double t_2 = ((x - t_1) - (a * t)) + (b * t);
	double tmp;
	if (t <= -2.7e+77) {
		tmp = t_2;
	} else if (t <= 3.2) {
		tmp = fma((y - 2.0), b, x) - (t_1 - a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 1.0) * z)
	t_2 = Float64(Float64(Float64(x - t_1) - Float64(a * t)) + Float64(b * t))
	tmp = 0.0
	if (t <= -2.7e+77)
		tmp = t_2;
	elseif (t <= 3.2)
		tmp = Float64(fma(Float64(y - 2.0), b, x) - Float64(t_1 - a));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - t$95$1), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+77], t$95$2, If[LessEqual[t, 3.2], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(t$95$1 - a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6999999999999998e77 or 3.2000000000000002 < t

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 77.6

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

   4. Applied rewrites 77.6%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 68.6

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

   7. Applied rewrites 68.6%

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

   if -2.6999999999999998e77 < t < 3.2000000000000002

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

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

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      5. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   7. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{elif}\;z \leq 0.0056:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \left(\left(y + t\right) - 2\right) \cdot b\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.6e+123)
   (fma (- 1.0 y) z (fma (- 1.0 t) a x))
   (if (<= z 0.0056)
     (fma (- (+ t y) 2.0) b (- x (* (- t 1.0) a)))
     (+ (fma (- 1.0 y) z (* (- (+ y t) 2.0) b)) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.6e+123) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else if (z <= 0.0056) {
		tmp = fma(((t + y) - 2.0), b, (x - ((t - 1.0) * a)));
	} else {
		tmp = fma((1.0 - y), z, (((y + t) - 2.0) * b)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.6e+123)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	elseif (z <= 0.0056)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(Float64(t - 1.0) * a)));
	else
		tmp = Float64(fma(Float64(1.0 - y), z, Float64(Float64(Float64(y + t) - 2.0) * b)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.6e+123], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0056], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000023e123

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate--l- N/A

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

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

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

      6. sub-negate-rev N/A

         \[\leadsto \left(x + \left(1 - y\right) \cdot z\right) - \left(t - 1\right) \cdot a \]

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. sub-negate-rev N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot \left(y - 1\right)\right) \cdot z + \left(x - \left(t - 1\right) \cdot a\right) \]

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

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

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

      16. sub-negate-rev N/A

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

      17. sub-flip N/A

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

      18. mul-1-neg N/A

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

      19. *-commutative N/A

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

   10. Applied rewrites 67.8%

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

   if -5.60000000000000023e123 < z < 0.00559999999999999994

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - a \cdot \left(t - 1\right)}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

      3. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot a\right) \]

      4. lift-*.f64 74.2

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

   6. Applied rewrites 74.2%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - \left(t - 1\right) \cdot a}\right) \]

   if 0.00559999999999999994 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right) + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto \left(b \cdot \left(\left(t + y\right) - 2\right) + z \cdot \left(1 - y\right)\right) + \color{blue}{x} \]

   6. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \left(\left(y + t\right) - 2\right) \cdot b\right) + x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 86.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ t_2 := \left(y - 1\right) \cdot z\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(-a\right) \cdot t\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) - \left(t\_2 - a\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+230}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)) (t_2 (* (- y 1.0) z)))
   (if (<= t -5.4e+79)
     (fma t_1 b (* (- a) t))
     (if (<= t 3.5e-9)
       (- (fma (- y 2.0) b x) (- t_2 a))
       (if (<= t 9e+230)
         (- (fma t_1 b x) t_2)
         (- (fma a (- t 1.0) (* z (- y 1.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double t_2 = (y - 1.0) * z;
	double tmp;
	if (t <= -5.4e+79) {
		tmp = fma(t_1, b, (-a * t));
	} else if (t <= 3.5e-9) {
		tmp = fma((y - 2.0), b, x) - (t_2 - a);
	} else if (t <= 9e+230) {
		tmp = fma(t_1, b, x) - t_2;
	} else {
		tmp = -fma(a, (t - 1.0), (z * (y - 1.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	t_2 = Float64(Float64(y - 1.0) * z)
	tmp = 0.0
	if (t <= -5.4e+79)
		tmp = fma(t_1, b, Float64(Float64(-a) * t));
	elseif (t <= 3.5e-9)
		tmp = Float64(fma(Float64(y - 2.0), b, x) - Float64(t_2 - a));
	elseif (t <= 9e+230)
		tmp = Float64(fma(t_1, b, x) - t_2);
	else
		tmp = Float64(-fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t, -5.4e+79], N[(t$95$1 * b + N[((-a) * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-9], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(t$95$2 - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+230], N[(N[(t$95$1 * b + x), $MachinePrecision] - t$95$2), $MachinePrecision], (-N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision])]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.3999999999999999e79

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{-1 \cdot \left(a \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-1 \cdot a\right) \cdot \color{blue}{t}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-1 \cdot a\right) \cdot \color{blue}{t}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(\mathsf{neg}\left(a\right)\right) \cdot t\right) \]

      4. lift-neg.f64 51.0

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-a\right) \cdot t\right) \]

   6. Applied rewrites 51.0%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(-a\right) \cdot t}\right) \]

   if -5.3999999999999999e79 < t < 3.4999999999999999e-9

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

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

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      5. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   7. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)} \]

   if 3.4999999999999999e-9 < t < 8.9999999999999998e230

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(t + y\right) - 2\right) + x\right) - \color{blue}{z} \cdot \left(y - 1\right) \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(y + t\right) - 2\right) + x\right) - z \cdot \left(y - 1\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - z \cdot \left(y - 1\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - \color{blue}{z} \cdot \left(y - 1\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - z \cdot \left(y - 1\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - z \cdot \left(y - 1\right) \]

      8. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - z \cdot \left(y - 1\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot \color{blue}{z} \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot z \]

      11. lift-*.f64 73.2

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot \color{blue}{z} \]

   4. Applied rewrites 73.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot z} \]

   if 8.9999999999999998e230 < t

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(t + y\right) - 2\right) - \color{blue}{\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a} \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      9. lower-+.f64 N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\left(t - 1\right) \cdot a + \color{blue}{z} \cdot \left(y - 1\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, \color{blue}{a}, z \cdot \left(y - 1\right)\right) \]

      12. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, z \cdot \left(y - 1\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      14. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      15. lift-*.f64 80.7

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)} \]

   5. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\left(t - 1\right) \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\left(t - 1\right) \cdot a + \left(y - 1\right) \cdot z\right)\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto -\left(\left(t - 1\right) \cdot a + \left(y - 1\right) \cdot z\right) \]

      5. *-commutative N/A

         \[\leadsto -\left(a \cdot \left(t - 1\right) + \left(y - 1\right) \cdot z\right) \]

      6. *-commutative N/A

         \[\leadsto -\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 53.6

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

   7. Applied rewrites 53.6%

      \[\leadsto -\mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{elif}\;z \leq 0.0056:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x - \left(t - 1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right) - \left(y - 1\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= z -5.6e+123)
     (fma (- 1.0 y) z (fma (- 1.0 t) a x))
     (if (<= z 0.0056)
       (fma t_1 b (- x (* (- t 1.0) a)))
       (- (fma t_1 b x) (* (- y 1.0) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if (z <= -5.6e+123) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else if (z <= 0.0056) {
		tmp = fma(t_1, b, (x - ((t - 1.0) * a)));
	} else {
		tmp = fma(t_1, b, x) - ((y - 1.0) * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (z <= -5.6e+123)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	elseif (z <= 0.0056)
		tmp = fma(t_1, b, Float64(x - Float64(Float64(t - 1.0) * a)));
	else
		tmp = Float64(fma(t_1, b, x) - Float64(Float64(y - 1.0) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -5.6e+123], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0056], N[(t$95$1 * b + N[(x - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * b + x), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000023e123

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate--l- N/A

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

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

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

      6. sub-negate-rev N/A

         \[\leadsto \left(x + \left(1 - y\right) \cdot z\right) - \left(t - 1\right) \cdot a \]

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. sub-negate-rev N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot \left(y - 1\right)\right) \cdot z + \left(x - \left(t - 1\right) \cdot a\right) \]

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

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

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

      16. sub-negate-rev N/A

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

      17. sub-flip N/A

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

      18. mul-1-neg N/A

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

      19. *-commutative N/A

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

   10. Applied rewrites 67.8%

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

   if -5.60000000000000023e123 < z < 0.00559999999999999994

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - a \cdot \left(t - 1\right)}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

      3. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot a\right) \]

      4. lift-*.f64 74.2

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

   6. Applied rewrites 74.2%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - \left(t - 1\right) \cdot a}\right) \]

   if 0.00559999999999999994 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(t + y\right) - 2\right) + x\right) - \color{blue}{z} \cdot \left(y - 1\right) \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(y + t\right) - 2\right) + x\right) - z \cdot \left(y - 1\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - z \cdot \left(y - 1\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - \color{blue}{z} \cdot \left(y - 1\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - z \cdot \left(y - 1\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - z \cdot \left(y - 1\right) \]

      8. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - z \cdot \left(y - 1\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot \color{blue}{z} \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot z \]

      11. lift-*.f64 73.2

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot \color{blue}{z} \]

   4. Applied rewrites 73.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(y - 1\right) \cdot z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right) - \left(t - 1\right) \cdot a\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x - \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -2.8e+63)
     (- (fma t_1 b x) (* (- t 1.0) a))
     (if (<= b -2.2e-104)
       (- (fma (- y 2.0) b x) (- (* (- y 1.0) z) a))
       (if (<= b 1.42e+85)
         (fma (- 1.0 y) z (fma (- 1.0 t) a x))
         (fma t_1 b (- x (- a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if (b <= -2.8e+63) {
		tmp = fma(t_1, b, x) - ((t - 1.0) * a);
	} else if (b <= -2.2e-104) {
		tmp = fma((y - 2.0), b, x) - (((y - 1.0) * z) - a);
	} else if (b <= 1.42e+85) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = fma(t_1, b, (x - -a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -2.8e+63)
		tmp = Float64(fma(t_1, b, x) - Float64(Float64(t - 1.0) * a));
	elseif (b <= -2.2e-104)
		tmp = Float64(fma(Float64(y - 2.0), b, x) - Float64(Float64(Float64(y - 1.0) * z) - a));
	elseif (b <= 1.42e+85)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = fma(t_1, b, Float64(x - Float64(-a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -2.8e+63], N[(N[(t$95$1 * b + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.2e-104], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.42e+85], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + N[(x - (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.79999999999999987e63

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - \color{blue}{a \cdot \left(t - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(t + y\right) - 2\right) + x\right) - \color{blue}{a} \cdot \left(t - 1\right) \]

      3. +-commutative N/A

         \[\leadsto \left(b \cdot \left(\left(y + t\right) - 2\right) + x\right) - a \cdot \left(t - 1\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - a \cdot \left(t - 1\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - \color{blue}{a} \cdot \left(t - 1\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right) - a \cdot \left(t - 1\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - a \cdot \left(t - 1\right) \]

      8. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - a \cdot \left(t - 1\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot \color{blue}{a} \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a \]

      11. lift-*.f64 73.2

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot \color{blue}{a} \]

   4. Applied rewrites 73.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a} \]

   if -2.79999999999999987e63 < b < -2.20000000000000012e-104

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

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

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      5. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   7. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)} \]

   if -2.20000000000000012e-104 < b < 1.42e85

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate--l- N/A

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

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

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

      6. sub-negate-rev N/A

         \[\leadsto \left(x + \left(1 - y\right) \cdot z\right) - \left(t - 1\right) \cdot a \]

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. sub-negate-rev N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot \left(y - 1\right)\right) \cdot z + \left(x - \left(t - 1\right) \cdot a\right) \]

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

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

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

      16. sub-negate-rev N/A

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

      17. sub-flip N/A

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

      18. mul-1-neg N/A

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

      19. *-commutative N/A

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

   10. Applied rewrites 67.8%

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

   if 1.42e85 < b

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - a \cdot \left(t - 1\right)}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

      3. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot a\right) \]

      4. lift-*.f64 74.2

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

   6. Applied rewrites 74.2%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - \left(t - 1\right) \cdot a}\right) \]

   7. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - -1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(\mathsf{neg}\left(a\right)\right)\right) \]

      2. lift-neg.f64 59.7

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   9. Applied rewrites 59.7%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right)\\ \mathbf{if}\;b \leq -2.95 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b (- x (- a)))))
   (if (<= b -2.95e+63)
     t_1
     (if (<= b -2.2e-104)
       (- (fma (- y 2.0) b x) (- (* (- y 1.0) z) a))
       (if (<= b 1.42e+85) (fma (- 1.0 y) z (fma (- 1.0 t) a x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, (x - -a));
	double tmp;
	if (b <= -2.95e+63) {
		tmp = t_1;
	} else if (b <= -2.2e-104) {
		tmp = fma((y - 2.0), b, x) - (((y - 1.0) * z) - a);
	} else if (b <= 1.42e+85) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-a)))
	tmp = 0.0
	if (b <= -2.95e+63)
		tmp = t_1;
	elseif (b <= -2.2e-104)
		tmp = Float64(fma(Float64(y - 2.0), b, x) - Float64(Float64(Float64(y - 1.0) * z) - a));
	elseif (b <= 1.42e+85)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.95e+63], t$95$1, If[LessEqual[b, -2.2e-104], N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.42e+85], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.95000000000000014e63 or 1.42e85 < b

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - a \cdot \left(t - 1\right)}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

      3. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot a\right) \]

      4. lift-*.f64 74.2

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

   6. Applied rewrites 74.2%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - \left(t - 1\right) \cdot a}\right) \]

   7. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - -1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(\mathsf{neg}\left(a\right)\right)\right) \]

      2. lift-neg.f64 59.7

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   9. Applied rewrites 59.7%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   if -2.95000000000000014e63 < b < -2.20000000000000012e-104

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

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

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      5. sub-negate-rev N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \left(x + \color{blue}{b} \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\color{blue}{x} + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(x + b \cdot \left(y - 2\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   7. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x\right) - \left(\left(y - 1\right) \cdot z - a\right)} \]

   if -2.20000000000000012e-104 < b < 1.42e85

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate--l- N/A

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

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

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

      6. sub-negate-rev N/A

         \[\leadsto \left(x + \left(1 - y\right) \cdot z\right) - \left(t - 1\right) \cdot a \]

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. sub-negate-rev N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot \left(y - 1\right)\right) \cdot z + \left(x - \left(t - 1\right) \cdot a\right) \]

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

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

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

      16. sub-negate-rev N/A

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

      17. sub-flip N/A

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

      18. mul-1-neg N/A

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

      19. *-commutative N/A

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

   10. Applied rewrites 67.8%

       \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 82.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right)\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b (- x (- a)))))
   (if (<= b -9.8e+146)
     t_1
     (if (<= b 1.42e+85) (fma (- 1.0 y) z (fma (- 1.0 t) a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, (x - -a));
	double tmp;
	if (b <= -9.8e+146) {
		tmp = t_1;
	} else if (b <= 1.42e+85) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-a)))
	tmp = 0.0
	if (b <= -9.8e+146)
		tmp = t_1;
	elseif (b <= 1.42e+85)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e+146], t$95$1, If[LessEqual[b, 1.42e+85], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.8000000000000003e146 or 1.42e85 < b

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - a \cdot \left(t - 1\right)}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

      3. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot a\right) \]

      4. lift-*.f64 74.2

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

   6. Applied rewrites 74.2%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - \left(t - 1\right) \cdot a}\right) \]

   7. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - -1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(\mathsf{neg}\left(a\right)\right)\right) \]

      2. lift-neg.f64 59.7

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   9. Applied rewrites 59.7%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   if -9.8000000000000003e146 < b < 1.42e85

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate--l- N/A

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

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

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

      6. sub-negate-rev N/A

         \[\leadsto \left(x + \left(1 - y\right) \cdot z\right) - \left(t - 1\right) \cdot a \]

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. sub-negate-rev N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(-1 \cdot \left(y - 1\right)\right) \cdot z + \left(x - \left(t - 1\right) \cdot a\right) \]

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

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

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

      16. sub-negate-rev N/A

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

      17. sub-flip N/A

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

      18. mul-1-neg N/A

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

      19. *-commutative N/A

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

   10. Applied rewrites 67.8%

       \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 71.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.023:\\ \;\;\;\;-\mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(b \cdot y - \left(y - 1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.023)
   (- (fma a (- t 1.0) (* z (- y 1.0))))
   (if (<= z 1.6e+64)
     (fma (- (+ t y) 2.0) b (- x (- a)))
     (+ a (- (* b y) (* (- y 1.0) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.023) {
		tmp = -fma(a, (t - 1.0), (z * (y - 1.0)));
	} else if (z <= 1.6e+64) {
		tmp = fma(((t + y) - 2.0), b, (x - -a));
	} else {
		tmp = a + ((b * y) - ((y - 1.0) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.023)
		tmp = Float64(-fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	elseif (z <= 1.6e+64)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-a)));
	else
		tmp = Float64(a + Float64(Float64(b * y) - Float64(Float64(y - 1.0) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.023], (-N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 1.6e+64], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-a)), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(b * y), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.023

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(t + y\right) - 2\right) - \color{blue}{\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a} \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      9. lower-+.f64 N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\left(t - 1\right) \cdot a + \color{blue}{z} \cdot \left(y - 1\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, \color{blue}{a}, z \cdot \left(y - 1\right)\right) \]

      12. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, z \cdot \left(y - 1\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      14. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      15. lift-*.f64 80.7

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)} \]

   5. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\left(t - 1\right) \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\left(\left(t - 1\right) \cdot a + \left(y - 1\right) \cdot z\right)\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto -\left(\left(t - 1\right) \cdot a + \left(y - 1\right) \cdot z\right) \]

      5. *-commutative N/A

         \[\leadsto -\left(a \cdot \left(t - 1\right) + \left(y - 1\right) \cdot z\right) \]

      6. *-commutative N/A

         \[\leadsto -\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 53.6

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

   7. Applied rewrites 53.6%

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

   if -0.023 < z < 1.60000000000000009e64

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - a \cdot \left(t - 1\right)}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

      3. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot a\right) \]

      4. lift-*.f64 74.2

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

   6. Applied rewrites 74.2%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - \left(t - 1\right) \cdot a}\right) \]

   7. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - -1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(\mathsf{neg}\left(a\right)\right)\right) \]

      2. lift-neg.f64 59.7

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   9. Applied rewrites 59.7%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   if 1.60000000000000009e64 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 49.1

         \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]

   10. Applied rewrites 49.1%

       \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 71.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.023:\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right) - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(b \cdot y - \left(y - 1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.023)
   (- (fma (- a) t a) (* z (- y 1.0)))
   (if (<= z 1.6e+64)
     (fma (- (+ t y) 2.0) b (- x (- a)))
     (+ a (- (* b y) (* (- y 1.0) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.023) {
		tmp = fma(-a, t, a) - (z * (y - 1.0));
	} else if (z <= 1.6e+64) {
		tmp = fma(((t + y) - 2.0), b, (x - -a));
	} else {
		tmp = a + ((b * y) - ((y - 1.0) * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.023)
		tmp = Float64(fma(Float64(-a), t, a) - Float64(z * Float64(y - 1.0)));
	elseif (z <= 1.6e+64)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-a)));
	else
		tmp = Float64(a + Float64(Float64(b * y) - Float64(Float64(y - 1.0) * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.023], N[(N[((-a) * t + a), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+64], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-a)), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(b * y), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.023

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(a \cdot t\right) + a\right) - z \cdot \left(y - 1\right) \]

      3. associate-*r* N/A

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot t + a\right) - z \cdot \left(y - 1\right) \]

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 53.2

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

   10. Applied rewrites 53.2%

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

   if -0.023 < z < 1.60000000000000009e64

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - a \cdot \left(t - 1\right)}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

      3. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot a\right) \]

      4. lift-*.f64 74.2

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

   6. Applied rewrites 74.2%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - \left(t - 1\right) \cdot a}\right) \]

   7. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - -1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(\mathsf{neg}\left(a\right)\right)\right) \]

      2. lift-neg.f64 59.7

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   9. Applied rewrites 59.7%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   if 1.60000000000000009e64 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 49.1

         \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]

   10. Applied rewrites 49.1%

       \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 68.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(b \cdot y - \left(y - 1\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.023:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- (* b y) (* (- y 1.0) z)))))
   (if (<= z -0.023)
     t_1
     (if (<= z 1.6e+64) (fma (- (+ t y) 2.0) b (- x (- a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + ((b * y) - ((y - 1.0) * z));
	double tmp;
	if (z <= -0.023) {
		tmp = t_1;
	} else if (z <= 1.6e+64) {
		tmp = fma(((t + y) - 2.0), b, (x - -a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(Float64(b * y) - Float64(Float64(y - 1.0) * z)))
	tmp = 0.0
	if (z <= -0.023)
		tmp = t_1;
	elseif (z <= 1.6e+64)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(x - Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(N[(b * y), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.023], t$95$1, If[LessEqual[z, 1.6e+64], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(x - (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.023 or 1.60000000000000009e64 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 49.1

         \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]

   10. Applied rewrites 49.1%

       \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]

   if -0.023 < z < 1.60000000000000009e64

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - a \cdot \left(t - 1\right)}\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

      3. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot a\right) \]

      4. lift-*.f64 74.2

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(t - 1\right) \cdot \color{blue}{a}\right) \]

   6. Applied rewrites 74.2%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{x - \left(t - 1\right) \cdot a}\right) \]

   7. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - -1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(\mathsf{neg}\left(a\right)\right)\right) \]

      2. lift-neg.f64 59.7

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, x - \left(-a\right)\right) \]

   9. Applied rewrites 59.7%

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

Alternative 16: 58.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(b \cdot y - \left(y - 1\right) \cdot z\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+57}:\\ \;\;\;\;a + \mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- (* b y) (* (- y 1.0) z)))))
   (if (<= z -4e-6)
     t_1
     (if (<= z 7.5e+57) (+ a (fma -2.0 b (* (- b a) t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + ((b * y) - ((y - 1.0) * z));
	double tmp;
	if (z <= -4e-6) {
		tmp = t_1;
	} else if (z <= 7.5e+57) {
		tmp = a + fma(-2.0, b, ((b - a) * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(Float64(b * y) - Float64(Float64(y - 1.0) * z)))
	tmp = 0.0
	if (z <= -4e-6)
		tmp = t_1;
	elseif (z <= 7.5e+57)
		tmp = Float64(a + fma(-2.0, b, Float64(Float64(b - a) * t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(N[(b * y), $MachinePrecision] - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e-6], t$95$1, If[LessEqual[z, 7.5e+57], N[(a + N[(-2.0 * b + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999982e-6 or 7.5000000000000006e57 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 49.1

         \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]

   10. Applied rewrites 49.1%

       \[\leadsto a + \left(b \cdot y - \left(y - 1\right) \cdot z\right) \]

   if -3.99999999999999982e-6 < z < 7.5000000000000006e57

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto a + \left(b \cdot \left(y - 2\right) + t \cdot \color{blue}{\left(b - a\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a + \left(\left(y - 2\right) \cdot b + t \cdot \left(b - a\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, t \cdot \left(b - a\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, t \cdot \left(b - a\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) \]

      5. lift--.f64 N/A

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) \]

      6. lift-*.f64 60.0

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) \]

   10. Applied rewrites 60.0%

       \[\leadsto a + \mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) \]

   11. Taylor expanded in y around 0

       \[\leadsto a + \mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 47.0%

       \[\leadsto a + \mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 57.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+69}:\\ \;\;\;\;a + \mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -1.02e+130)
     t_1
     (if (<= z 1.8e+69) (+ a (fma -2.0 b (* (- b a) t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -1.02e+130) {
		tmp = t_1;
	} else if (z <= 1.8e+69) {
		tmp = a + fma(-2.0, b, ((b - a) * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -1.02e+130)
		tmp = t_1;
	elseif (z <= 1.8e+69)
		tmp = Float64(a + fma(-2.0, b, Float64(Float64(b - a) * t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.02e+130], t$95$1, If[LessEqual[z, 1.8e+69], N[(a + N[(-2.0 * b + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.01999999999999999e130 or 1.8000000000000001e69 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around inf

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

      1. sub-negate-rev N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - y\right) \cdot z \]

      7. lower--.f64 28.5

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 28.5%

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

   if -1.01999999999999999e130 < z < 1.8000000000000001e69

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto a + \left(b \cdot \left(y - 2\right) + t \cdot \color{blue}{\left(b - a\right)}\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto a + \left(\left(y - 2\right) \cdot b + t \cdot \left(b - a\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, t \cdot \left(b - a\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, t \cdot \left(b - a\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) \]

      5. lift--.f64 N/A

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) \]

      6. lift-*.f64 60.0

         \[\leadsto a + \mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) \]

   10. Applied rewrites 60.0%

       \[\leadsto a + \mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) \]

   11. Taylor expanded in y around 0

       \[\leadsto a + \mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 47.0%

       \[\leadsto a + \mathsf{fma}\left(-2, b, \left(b - a\right) \cdot t\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 48.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-289}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -2.6e+87)
     t_1
     (if (<= z -5.1e-289)
       (* (- 1.0 t) a)
       (if (<= z 8.5e+63) (* (- (+ t y) 2.0) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -2.6e+87) {
		tmp = t_1;
	} else if (z <= -5.1e-289) {
		tmp = (1.0 - t) * a;
	} else if (z <= 8.5e+63) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - y) * z
    if (z <= (-2.6d+87)) then
        tmp = t_1
    else if (z <= (-5.1d-289)) then
        tmp = (1.0d0 - t) * a
    else if (z <= 8.5d+63) then
        tmp = ((t + y) - 2.0d0) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -2.6e+87) {
		tmp = t_1;
	} else if (z <= -5.1e-289) {
		tmp = (1.0 - t) * a;
	} else if (z <= 8.5e+63) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	tmp = 0
	if z <= -2.6e+87:
		tmp = t_1
	elif z <= -5.1e-289:
		tmp = (1.0 - t) * a
	elif z <= 8.5e+63:
		tmp = ((t + y) - 2.0) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -2.6e+87)
		tmp = t_1;
	elseif (z <= -5.1e-289)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (z <= 8.5e+63)
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	tmp = 0.0;
	if (z <= -2.6e+87)
		tmp = t_1;
	elseif (z <= -5.1e-289)
		tmp = (1.0 - t) * a;
	elseif (z <= 8.5e+63)
		tmp = ((t + y) - 2.0) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.6e+87], t$95$1, If[LessEqual[z, -5.1e-289], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, 8.5e+63], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999998e87 or 8.5000000000000004e63 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around inf

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

      1. sub-negate-rev N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - y\right) \cdot z \]

      7. lower--.f64 28.5

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 28.5%

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

   if -2.59999999999999998e87 < z < -5.0999999999999996e-289

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   if -5.0999999999999996e-289 < z < 8.5000000000000004e63

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1 \cdot a} + z \cdot \left(y - 1\right)\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, b \cdot \left(y - 2\right)\right) - \left(\color{blue}{-1} \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(z \cdot \left(y - 1\right) + \color{blue}{-1 \cdot a}\right)\right) \]

      12. *-commutative N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \left(\left(y - 1\right) \cdot z + \color{blue}{-1} \cdot a\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, \color{blue}{z}, -1 \cdot a\right)\right) \]

      14. lift--.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -1 \cdot a\right)\right) \]

      15. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, \mathsf{neg}\left(a\right)\right)\right) \]

      16. lower-neg.f64 96.2

          \[\leadsto x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right) \]

   4. Applied rewrites 96.2%

      \[\leadsto \color{blue}{x + \left(\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right) - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(a + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto a + \left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) - \color{blue}{z \cdot \left(y - 1\right)}\right) \]

      3. +-commutative N/A

         \[\leadsto a + \left(\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right) - z \cdot \left(\color{blue}{y} - 1\right)\right) \]

      4. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + b \cdot \left(y - 2\right)\right) - z \cdot \left(y - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \left(y - 1\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto a + \left(\left(\left(b - a\right) \cdot t + \left(y - 2\right) \cdot b\right) - z \cdot \color{blue}{\left(y - 1\right)}\right) \]

   7. Applied rewrites 81.5%

      \[\leadsto a + \color{blue}{\left(\mathsf{fma}\left(y - 2, b, \left(b - a\right) \cdot t\right) - \left(y - 1\right) \cdot z\right)} \]

   8. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot \color{blue}{b} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot \color{blue}{b} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b \]

      4. lift-+.f64 36.7

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b \]

   10. Applied rewrites 36.7%

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

Alternative 19: 46.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -8 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \left(-a\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -8e+40)
     t_1
     (if (<= z 1.26e+64) (fma (- t 2.0) b (* (- a) t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -8e+40) {
		tmp = t_1;
	} else if (z <= 1.26e+64) {
		tmp = fma((t - 2.0), b, (-a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -8e+40)
		tmp = t_1;
	elseif (z <= 1.26e+64)
		tmp = fma(Float64(t - 2.0), b, Float64(Float64(-a) * t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -8e+40], t$95$1, If[LessEqual[z, 1.26e+64], N[(N[(t - 2.0), $MachinePrecision] * b + N[((-a) * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000024e40 or 1.26e64 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around inf

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

      1. sub-negate-rev N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - y\right) \cdot z \]

      7. lower--.f64 28.5

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 28.5%

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

   if -8.00000000000000024e40 < z < 1.26e64

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      10. lift--.f64 N/A

          \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      11. +-commutative N/A

          \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]

      17. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - a \cdot \left(t - 1\right)}\right) \]

   3. Applied rewrites 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - y, z, x\right) - \left(t - 1\right) \cdot a\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{-1 \cdot \left(a \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-1 \cdot a\right) \cdot \color{blue}{t}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-1 \cdot a\right) \cdot \color{blue}{t}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(\mathsf{neg}\left(a\right)\right) \cdot t\right) \]

      4. lift-neg.f64 51.0

         \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-a\right) \cdot t\right) \]

   6. Applied rewrites 51.0%

      \[\leadsto \mathsf{fma}\left(\left(t + y\right) - 2, b, \color{blue}{\left(-a\right) \cdot t}\right) \]

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{t} - 2, b, \left(-a\right) \cdot t\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 37.4%

      \[\leadsto \mathsf{fma}\left(\color{blue}{t} - 2, b, \left(-a\right) \cdot t\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 43.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-31}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+63}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -2.6e+87)
     t_1
     (if (<= z 3.6e-31)
       (* (- 1.0 t) a)
       (if (<= z 7.5e+63) (* (- b a) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -2.6e+87) {
		tmp = t_1;
	} else if (z <= 3.6e-31) {
		tmp = (1.0 - t) * a;
	} else if (z <= 7.5e+63) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - y) * z
    if (z <= (-2.6d+87)) then
        tmp = t_1
    else if (z <= 3.6d-31) then
        tmp = (1.0d0 - t) * a
    else if (z <= 7.5d+63) then
        tmp = (b - a) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -2.6e+87) {
		tmp = t_1;
	} else if (z <= 3.6e-31) {
		tmp = (1.0 - t) * a;
	} else if (z <= 7.5e+63) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	tmp = 0
	if z <= -2.6e+87:
		tmp = t_1
	elif z <= 3.6e-31:
		tmp = (1.0 - t) * a
	elif z <= 7.5e+63:
		tmp = (b - a) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -2.6e+87)
		tmp = t_1;
	elseif (z <= 3.6e-31)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (z <= 7.5e+63)
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	tmp = 0.0;
	if (z <= -2.6e+87)
		tmp = t_1;
	elseif (z <= 3.6e-31)
		tmp = (1.0 - t) * a;
	elseif (z <= 7.5e+63)
		tmp = (b - a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.6e+87], t$95$1, If[LessEqual[z, 3.6e-31], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[z, 7.5e+63], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999998e87 or 7.5000000000000005e63 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around inf

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

      1. sub-negate-rev N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - y\right) \cdot z \]

      7. lower--.f64 28.5

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 28.5%

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

   if -2.59999999999999998e87 < z < 3.60000000000000004e-31

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   if 3.60000000000000004e-31 < z < 7.5000000000000005e63

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 32.0

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 32.0%

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

Alternative 21: 42.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0076:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -2.6e+87) t_1 (if (<= z 0.0076) (* (- 1.0 t) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -2.6e+87) {
		tmp = t_1;
	} else if (z <= 0.0076) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - y) * z
    if (z <= (-2.6d+87)) then
        tmp = t_1
    else if (z <= 0.0076d0) then
        tmp = (1.0d0 - t) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -2.6e+87) {
		tmp = t_1;
	} else if (z <= 0.0076) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	tmp = 0
	if z <= -2.6e+87:
		tmp = t_1
	elif z <= 0.0076:
		tmp = (1.0 - t) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -2.6e+87)
		tmp = t_1;
	elseif (z <= 0.0076)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	tmp = 0.0;
	if (z <= -2.6e+87)
		tmp = t_1;
	elseif (z <= 0.0076)
		tmp = (1.0 - t) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.6e+87], t$95$1, If[LessEqual[z, 0.0076], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999998e87 or 0.00759999999999999998 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around inf

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

      1. sub-negate-rev N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - y\right) \cdot z \]

      7. lower--.f64 28.5

         \[\leadsto \left(1 - y\right) \cdot z \]

   4. Applied rewrites 28.5%

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

   if -2.59999999999999998e87 < z < 0.00759999999999999998

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 34.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot z\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.008:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y) z)))
   (if (<= z -1.8e+129) t_1 (if (<= z 0.008) (* (- 1.0 t) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (z <= -1.8e+129) {
		tmp = t_1;
	} else if (z <= 0.008) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y * z
    if (z <= (-1.8d+129)) then
        tmp = t_1
    else if (z <= 0.008d0) then
        tmp = (1.0d0 - t) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (z <= -1.8e+129) {
		tmp = t_1;
	} else if (z <= 0.008) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -y * z
	tmp = 0
	if z <= -1.8e+129:
		tmp = t_1
	elif z <= 0.008:
		tmp = (1.0 - t) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-y) * z)
	tmp = 0.0
	if (z <= -1.8e+129)
		tmp = t_1;
	elseif (z <= 0.008)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -y * z;
	tmp = 0.0;
	if (z <= -1.8e+129)
		tmp = t_1;
	elseif (z <= 0.008)
		tmp = (1.0 - t) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z), $MachinePrecision]}, If[LessEqual[z, -1.8e+129], t$95$1, If[LessEqual[z, 0.008], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e129 or 0.0080000000000000002 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.4

         \[\leadsto \left(b - z\right) \cdot y \]

   4. Applied rewrites 33.4%

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

   5. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.0%

      \[\leadsto b \cdot y \]

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y\right) \cdot z \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot z \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(-y\right) \cdot z \]

      4. lower-*.f64 19.4

         \[\leadsto \left(-y\right) \cdot z \]

   10. Applied rewrites 19.4%

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

   if -1.8000000000000001e129 < z < 0.0080000000000000002

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 29.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot z\\ \mathbf{if}\;y \leq -700000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-110}:\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y) z)))
   (if (<= y -700000000.0)
     t_1
     (if (<= y 1.45e-110) (* (- t) a) (if (<= y 5.4e+68) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (y <= -700000000.0) {
		tmp = t_1;
	} else if (y <= 1.45e-110) {
		tmp = -t * a;
	} else if (y <= 5.4e+68) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y * z
    if (y <= (-700000000.0d0)) then
        tmp = t_1
    else if (y <= 1.45d-110) then
        tmp = -t * a
    else if (y <= 5.4d+68) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (y <= -700000000.0) {
		tmp = t_1;
	} else if (y <= 1.45e-110) {
		tmp = -t * a;
	} else if (y <= 5.4e+68) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -y * z
	tmp = 0
	if y <= -700000000.0:
		tmp = t_1
	elif y <= 1.45e-110:
		tmp = -t * a
	elif y <= 5.4e+68:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-y) * z)
	tmp = 0.0
	if (y <= -700000000.0)
		tmp = t_1;
	elseif (y <= 1.45e-110)
		tmp = Float64(Float64(-t) * a);
	elseif (y <= 5.4e+68)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -y * z;
	tmp = 0.0;
	if (y <= -700000000.0)
		tmp = t_1;
	elseif (y <= 1.45e-110)
		tmp = -t * a;
	elseif (y <= 5.4e+68)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z), $MachinePrecision]}, If[LessEqual[y, -700000000.0], t$95$1, If[LessEqual[y, 1.45e-110], N[((-t) * a), $MachinePrecision], If[LessEqual[y, 5.4e+68], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e8 or 5.39999999999999982e68 < y

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.4

         \[\leadsto \left(b - z\right) \cdot y \]

   4. Applied rewrites 33.4%

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

   5. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.0%

      \[\leadsto b \cdot y \]

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y\right) \cdot z \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot z \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(-y\right) \cdot z \]

      4. lower-*.f64 19.4

         \[\leadsto \left(-y\right) \cdot z \]

   10. Applied rewrites 19.4%

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

   if -7e8 < y < 1.4500000000000001e-110

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto \left(-1 \cdot t\right) \cdot a \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(t\right)\right) \cdot a \]

      2. lower-neg.f64 19.3

         \[\leadsto \left(-t\right) \cdot a \]

   7. Applied rewrites 19.3%

      \[\leadsto \left(-t\right) \cdot a \]

   if 1.4500000000000001e-110 < y < 5.39999999999999982e68

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(t + y\right) - 2\right) - \color{blue}{\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a} \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      9. lower-+.f64 N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\left(t - 1\right) \cdot a + \color{blue}{z} \cdot \left(y - 1\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, \color{blue}{a}, z \cdot \left(y - 1\right)\right) \]

      12. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, z \cdot \left(y - 1\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      14. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      15. lift-*.f64 80.7

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 16.1%

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

Alternative 24: 27.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot z\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y) z))) (if (<= z -3.3e+99) t_1 (if (<= z 9.2e+35) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (z <= -3.3e+99) {
		tmp = t_1;
	} else if (z <= 9.2e+35) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y * z
    if (z <= (-3.3d+99)) then
        tmp = t_1
    else if (z <= 9.2d+35) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (z <= -3.3e+99) {
		tmp = t_1;
	} else if (z <= 9.2e+35) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -y * z
	tmp = 0
	if z <= -3.3e+99:
		tmp = t_1
	elif z <= 9.2e+35:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-y) * z)
	tmp = 0.0
	if (z <= -3.3e+99)
		tmp = t_1;
	elseif (z <= 9.2e+35)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -y * z;
	tmp = 0.0;
	if (z <= -3.3e+99)
		tmp = t_1;
	elseif (z <= 9.2e+35)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z), $MachinePrecision]}, If[LessEqual[z, -3.3e+99], t$95$1, If[LessEqual[z, 9.2e+35], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e99 or 9.1999999999999993e35 < z

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.4

         \[\leadsto \left(b - z\right) \cdot y \]

   4. Applied rewrites 33.4%

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

   5. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.0%

      \[\leadsto b \cdot y \]

   8. Taylor expanded in z around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y\right) \cdot z \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot z \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(-y\right) \cdot z \]

      4. lower-*.f64 19.4

         \[\leadsto \left(-y\right) \cdot z \]

   10. Applied rewrites 19.4%

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

   if -3.2999999999999999e99 < z < 9.1999999999999993e35

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(t + y\right) - 2\right) - \color{blue}{\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a} \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      9. lower-+.f64 N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\left(t - 1\right) \cdot a + \color{blue}{z} \cdot \left(y - 1\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, \color{blue}{a}, z \cdot \left(y - 1\right)\right) \]

      12. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, z \cdot \left(y - 1\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      14. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      15. lift-*.f64 80.7

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 16.1%

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

Alternative 25: 21.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+164}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-206}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+66}:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.2e+164) x (if (<= x 4.3e-206) a (if (<= x 7.5e+66) (* b y) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.2e+164) {
		tmp = x;
	} else if (x <= 4.3e-206) {
		tmp = a;
	} else if (x <= 7.5e+66) {
		tmp = b * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.2d+164)) then
        tmp = x
    else if (x <= 4.3d-206) then
        tmp = a
    else if (x <= 7.5d+66) then
        tmp = b * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.2e+164) {
		tmp = x;
	} else if (x <= 4.3e-206) {
		tmp = a;
	} else if (x <= 7.5e+66) {
		tmp = b * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.2e+164:
		tmp = x
	elif x <= 4.3e-206:
		tmp = a
	elif x <= 7.5e+66:
		tmp = b * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.2e+164)
		tmp = x;
	elseif (x <= 4.3e-206)
		tmp = a;
	elseif (x <= 7.5e+66)
		tmp = Float64(b * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.2e+164)
		tmp = x;
	elseif (x <= 4.3e-206)
		tmp = a;
	elseif (x <= 7.5e+66)
		tmp = b * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.2e+164], x, If[LessEqual[x, 4.3e-206], a, If[LessEqual[x, 7.5e+66], N[(b * y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.20000000000000032e164 or 7.50000000000000024e66 < x

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(t + y\right) - 2\right) - \color{blue}{\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a} \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      9. lower-+.f64 N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\left(t - 1\right) \cdot a + \color{blue}{z} \cdot \left(y - 1\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, \color{blue}{a}, z \cdot \left(y - 1\right)\right) \]

      12. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, z \cdot \left(y - 1\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      14. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      15. lift-*.f64 80.7

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 16.1%

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

   if -8.20000000000000032e164 < x < 4.30000000000000025e-206

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 10.9%

      \[\leadsto a \]

   if 4.30000000000000025e-206 < x < 7.50000000000000024e66

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.4

         \[\leadsto \left(b - z\right) \cdot y \]

   4. Applied rewrites 33.4%

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

   5. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.0%

      \[\leadsto b \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 26: 19.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+164}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-15}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.2e+164) x (if (<= x 2.9e-15) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.2e+164) {
		tmp = x;
	} else if (x <= 2.9e-15) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.2d+164)) then
        tmp = x
    else if (x <= 2.9d-15) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.2e+164) {
		tmp = x;
	} else if (x <= 2.9e-15) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.2e+164:
		tmp = x
	elif x <= 2.9e-15:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.2e+164)
		tmp = x;
	elseif (x <= 2.9e-15)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.2e+164)
		tmp = x;
	elseif (x <= 2.9e-15)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.2e+164], x, If[LessEqual[x, 2.9e-15], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.20000000000000032e164 or 2.90000000000000019e-15 < x

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(t + y\right) - 2\right) - \color{blue}{\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a} \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      5. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

      7. lift-+.f64 N/A

         \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      9. lower-+.f64 N/A

         \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\left(t - 1\right) \cdot a + \color{blue}{z} \cdot \left(y - 1\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, \color{blue}{a}, z \cdot \left(y - 1\right)\right) \]

      12. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, z \cdot \left(y - 1\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      14. lift--.f64 N/A

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

      15. lift-*.f64 80.7

          \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

   4. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 16.1%

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

   if -8.20000000000000032e164 < x < 2.90000000000000019e-15

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. sub-negate-rev N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \]

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a \]

      6. sub-negate-rev N/A

         \[\leadsto \left(1 - t\right) \cdot a \]

      7. lower--.f64 28.1

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 28.1%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 10.9%

      \[\leadsto a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 27: 16.1% accurate, 28.4× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
3. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto b \cdot \left(\left(t + y\right) - 2\right) - \color{blue}{\left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   2. *-commutative N/A

      \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

   4. lift--.f64 N/A

      \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a} \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

   5. lift-+.f64 N/A

      \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

   6. lift-*.f64 N/A

      \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(\color{blue}{a \cdot \left(t - 1\right)} + z \cdot \left(y - 1\right)\right) \]

   7. lift-+.f64 N/A

      \[\leadsto \left(\left(y + t\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

   8. +-commutative N/A

      \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

   9. lower-+.f64 N/A

      \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \left(\left(t - 1\right) \cdot a + \color{blue}{z} \cdot \left(y - 1\right)\right) \]

   11. lower-fma.f64 N/A

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, \color{blue}{a}, z \cdot \left(y - 1\right)\right) \]

   12. lift--.f64 N/A

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, z \cdot \left(y - 1\right)\right) \]

   13. *-commutative N/A

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

   14. lift--.f64 N/A

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

   15. lift-*.f64 80.7

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right) \]

4. Applied rewrites 80.7%

   \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)} \]

5. Taylor expanded in x around inf

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

7. Applied rewrites 16.1%

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

Reproduce

herbie shell --seed 2025134 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))