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

Percentage Accurate: 95.1% → 98.1%

Time: 7.3s

Alternatives: 25

Speedup: 1.1×

• 35.5% 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: 95.1% 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: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 100.0

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

   8. Applied rewrites 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 30.8

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

   5. Applied rewrites 30.8%

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

   6. Taylor expanded in a around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift--.f64 53.8

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

   8. Applied rewrites 53.8%

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

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lift-*.f64 N/A

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

       3. lift--.f64 76.9

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

   11. Applied rewrites 76.9%

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

Alternative 2: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+35}:\\ \;\;\;\;\left(x + z\right) + \mathsf{fma}\left(1 - t, a, \left(b - z\right) \cdot y\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+56}:\\ \;\;\;\;\left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(1 - t\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.2e+35)
   (+ (+ x z) (fma (- 1.0 t) a (* (- b z) y)))
   (if (<= a 8.5e+56)
     (- (+ (fma (- b z) y (* (- t 2.0) b)) x) (- z))
     (fma (- (+ t y) 2.0) b (* (- 1.0 t) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.2e+35) {
		tmp = (x + z) + fma((1.0 - t), a, ((b - z) * y));
	} else if (a <= 8.5e+56) {
		tmp = (fma((b - z), y, ((t - 2.0) * b)) + x) - -z;
	} else {
		tmp = fma(((t + y) - 2.0), b, ((1.0 - t) * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.2e+35)
		tmp = Float64(Float64(x + z) + fma(Float64(1.0 - t), a, Float64(Float64(b - z) * y)));
	elseif (a <= 8.5e+56)
		tmp = Float64(Float64(fma(Float64(b - z), y, Float64(Float64(t - 2.0) * b)) + x) - Float64(-z));
	else
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(1.0 - t) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.2e+35], N[(N[(x + z), $MachinePrecision] + N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+56], N[(N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - (-z)), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.19999999999999973e35

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 91.9

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift--.f64 93.5

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

   8. Applied rewrites 93.5%

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

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lift-*.f64 N/A

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

       3. lift--.f64 95.1

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

   11. Applied rewrites 95.1%

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

   if -6.19999999999999973e35 < a < 8.4999999999999998e56

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 97.9

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 94.8

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

   8. Applied rewrites 94.8%

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

   if 8.4999999999999998e56 < a

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 35.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 35.5

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

   7. Applied rewrites 35.5%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 92.1

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

   10. Applied rewrites 92.1%

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

Alternative 3: 88.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(1 - t\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+117}:\\ \;\;\;\;\left(x + z\right) + \mathsf{fma}\left(1 - t, a, \left(b - z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.8e+55)
   (fma (- (+ t y) 2.0) b (* (- 1.0 t) a))
   (if (<= b 6.5e+117)
     (+ (+ x z) (fma (- 1.0 t) a (* (- b z) y)))
     (+ (* (- 1.0 y) z) (* (- (+ y t) 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e+55) {
		tmp = fma(((t + y) - 2.0), b, ((1.0 - t) * a));
	} else if (b <= 6.5e+117) {
		tmp = (x + z) + fma((1.0 - t), a, ((b - z) * y));
	} else {
		tmp = ((1.0 - y) * z) + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.8e+55)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(1.0 - t) * a));
	elseif (b <= 6.5e+117)
		tmp = Float64(Float64(x + z) + fma(Float64(1.0 - t), a, Float64(Float64(b - z) * y)));
	else
		tmp = Float64(Float64(Float64(1.0 - y) * z) + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.8e+55], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+117], N[(N[(x + z), $MachinePrecision] + N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.8000000000000001e55

   1. Initial program 85.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 71.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 71.8

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

   7. Applied rewrites 71.8%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 86.5

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

   10. Applied rewrites 86.5%

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

   if -2.8000000000000001e55 < b < 6.5000000000000004e117

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.3

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift--.f64 100.0

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lift-*.f64 N/A

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

       3. lift--.f64 94.5

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

   11. Applied rewrites 94.5%

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

   if 6.5000000000000004e117 < b

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 86.8

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

   5. Applied rewrites 86.8%

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

Alternative 4: 97.3% accurate, 1.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 48.8%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift--.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lift--.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 48.8

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

7. Applied rewrites 48.8%

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

8. Taylor expanded in t around 0

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

   1. lower--.f64 N/A

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

   2. +-commutative N/A

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

   3. associate-*r* N/A

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

   4. lower-fma.f64 N/A

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

   5. mul-1-neg N/A

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

   6. lower-neg.f64 N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lower--.f64 N/A

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

   10. mul-1-neg N/A

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

   11. lower-neg.f64 97.6

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

10. Applied rewrites 97.6%

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

Alternative 5: 44.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, a\right)\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-161}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-56}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- a) t a)))
   (if (<= a -2.15e+145)
     t_1
     (if (<= a 1.6e-161)
       (fma y b x)
       (if (<= a 2e-56)
         (* (- 1.0 y) z)
         (if (<= a 4.2e+56) (fma y b x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-a, t, a);
	double tmp;
	if (a <= -2.15e+145) {
		tmp = t_1;
	} else if (a <= 1.6e-161) {
		tmp = fma(y, b, x);
	} else if (a <= 2e-56) {
		tmp = (1.0 - y) * z;
	} else if (a <= 4.2e+56) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-a), t, a)
	tmp = 0.0
	if (a <= -2.15e+145)
		tmp = t_1;
	elseif (a <= 1.6e-161)
		tmp = fma(y, b, x);
	elseif (a <= 2e-56)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (a <= 4.2e+56)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t + a), $MachinePrecision]}, If[LessEqual[a, -2.15e+145], t$95$1, If[LessEqual[a, 1.6e-161], N[(y * b + x), $MachinePrecision], If[LessEqual[a, 2e-56], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 4.2e+56], N[(y * b + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.14999999999999999e145 or 4.20000000000000034e56 < a

   1. Initial program 91.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.7

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

   5. Applied rewrites 68.7%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), t, a\right) \]

      5. lift-neg.f64 68.7

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

   8. Applied rewrites 68.7%

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

   if -2.14999999999999999e145 < a < 1.59999999999999993e-161 or 2.0000000000000001e-56 < a < 4.20000000000000034e56

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 63.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 63.0

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

   7. Applied rewrites 63.0%

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

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 44.1%

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

   if 1.59999999999999993e-161 < a < 2.0000000000000001e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.2

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

   5. Applied rewrites 52.2%

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

Alternative 6: 43.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, a\right)\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-159}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- a) t a)))
   (if (<= a -2.15e+145)
     t_1
     (if (<= a 8.5e-159)
       (fma y b x)
       (if (<= a 1.6e-57) (* (- z) y) (if (<= a 4.2e+56) (fma y b x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-a, t, a);
	double tmp;
	if (a <= -2.15e+145) {
		tmp = t_1;
	} else if (a <= 8.5e-159) {
		tmp = fma(y, b, x);
	} else if (a <= 1.6e-57) {
		tmp = -z * y;
	} else if (a <= 4.2e+56) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-a), t, a)
	tmp = 0.0
	if (a <= -2.15e+145)
		tmp = t_1;
	elseif (a <= 8.5e-159)
		tmp = fma(y, b, x);
	elseif (a <= 1.6e-57)
		tmp = Float64(Float64(-z) * y);
	elseif (a <= 4.2e+56)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t + a), $MachinePrecision]}, If[LessEqual[a, -2.15e+145], t$95$1, If[LessEqual[a, 8.5e-159], N[(y * b + x), $MachinePrecision], If[LessEqual[a, 1.6e-57], N[((-z) * y), $MachinePrecision], If[LessEqual[a, 4.2e+56], N[(y * b + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.14999999999999999e145 or 4.20000000000000034e56 < a

   1. Initial program 91.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.7

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

   5. Applied rewrites 68.7%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), t, a\right) \]

      5. lift-neg.f64 68.7

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

   8. Applied rewrites 68.7%

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

   if -2.14999999999999999e145 < a < 8.4999999999999998e-159 or 1.6e-57 < a < 4.20000000000000034e56

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 62.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 62.2

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

   7. Applied rewrites 62.2%

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

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 43.5%

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

   if 8.4999999999999998e-159 < a < 1.6e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 45.4

         \[\leadsto \left(b - z\right) \cdot y \]

   5. Applied rewrites 45.4%

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

   6. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot z\right) \cdot y \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(z\right)\right) \cdot y \]

      2. lower-neg.f64 44.9

         \[\leadsto \left(-z\right) \cdot y \]

   8. Applied rewrites 44.9%

      \[\leadsto \left(-z\right) \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 85.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(1 - t\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+19}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + t\_1 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -1.15e+53)
     (fma t_1 b (* (- 1.0 t) a))
     (if (<= b 4e+19)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (+ (+ x z) (* t_1 b))))))

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 <= -1.15e+53) {
		tmp = fma(t_1, b, ((1.0 - t) * a));
	} else if (b <= 4e+19) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = (x + z) + (t_1 * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -1.15e+53)
		tmp = fma(t_1, b, Float64(Float64(1.0 - t) * a));
	elseif (b <= 4e+19)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = Float64(Float64(x + z) + Float64(t_1 * b));
	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, -1.15e+53], N[(t$95$1 * b + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+19], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(t$95$1 * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1500000000000001e53

   1. Initial program 85.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 70.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 70.6

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

   7. Applied rewrites 70.6%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 86.7

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

   10. Applied rewrites 86.7%

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

   if -1.1500000000000001e53 < b < 4e19

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 90.9

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

   5. Applied rewrites 90.9%

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

   if 4e19 < b

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.3

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift--.f64 98.1

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

   8. Applied rewrites 98.1%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lift--.f64 N/A

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

       4. lift-+.f64 83.5

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

   11. Applied rewrites 83.5%

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

Alternative 8: 83.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -9 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+19}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + t\_1 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -9e+143)
     (fma t_1 b a)
     (if (<= b 4e+19)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (+ (+ x z) (* t_1 b))))))

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 <= -9e+143) {
		tmp = fma(t_1, b, a);
	} else if (b <= 4e+19) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else {
		tmp = (x + z) + (t_1 * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -9e+143)
		tmp = fma(t_1, b, a);
	elseif (b <= 4e+19)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = Float64(Float64(x + z) + Float64(t_1 * b));
	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, -9e+143], N[(t$95$1 * b + a), $MachinePrecision], If[LessEqual[b, 4e+19], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(t$95$1 * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999993e143

   1. Initial program 89.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 85.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 85.7

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

   7. Applied rewrites 85.7%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 90.9

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

   10. Applied rewrites 90.9%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 88.5%

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

   if -8.9999999999999993e143 < b < 4e19

   1. Initial program 95.7%

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

   3. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 88.2

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

   5. Applied rewrites 88.2%

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

   if 4e19 < b

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 96.3

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift--.f64 98.1

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

   8. Applied rewrites 98.1%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lift--.f64 N/A

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

       4. lift-+.f64 83.5

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

   11. Applied rewrites 83.5%

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

Alternative 9: 97.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

3. Taylor expanded in y around 0

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

   1. lower--.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lower--.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower--.f64 N/A

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

   11. +-commutative N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lift--.f64 N/A

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

   15. mul-1-neg N/A

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

   16. lower-neg.f64 96.5

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

5. Applied rewrites 96.5%

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

6. Taylor expanded in a around 0

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

   1. associate-+r+ N/A

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

   2. lower-+.f64 N/A

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

   3. lower-+.f64 N/A

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

   4. *-commutative N/A

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

   5. *-commutative N/A

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

   6. *-commutative N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lower--.f64 N/A

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

   10. +-commutative N/A

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

   11. *-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. lift--.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-*.f64 N/A

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

   16. lift--.f64 96.8

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

8. Applied rewrites 96.8%

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

Alternative 10: 71.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+39} \lor \neg \left(a \leq 8.5 \cdot 10^{+56}\right):\\ \;\;\;\;\mathsf{fma}\left(y, b, \left(1 - t\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + \left(\left(t + y\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.6e+39) (not (<= a 8.5e+56)))
   (fma y b (* (- 1.0 t) a))
   (+ (+ x z) (* (- (+ t y) 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.6e+39) || !(a <= 8.5e+56)) {
		tmp = fma(y, b, ((1.0 - t) * a));
	} else {
		tmp = (x + z) + (((t + y) - 2.0) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.6e+39) || !(a <= 8.5e+56))
		tmp = fma(y, b, Float64(Float64(1.0 - t) * a));
	else
		tmp = Float64(Float64(x + z) + Float64(Float64(Float64(t + y) - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.6e+39], N[Not[LessEqual[a, 8.5e+56]], $MachinePrecision]], N[(y * b + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.59999999999999996e39 or 8.4999999999999998e56 < a

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 31.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 32.0

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

   7. Applied rewrites 32.0%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 80.2

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

   10. Applied rewrites 80.2%

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

   11. Taylor expanded in y around inf

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

   13. Applied rewrites 75.9%

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

   if -1.59999999999999996e39 < a < 8.4999999999999998e56

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 97.9

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift--.f64 99.3

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

   8. Applied rewrites 99.3%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lift--.f64 N/A

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

       4. lift-+.f64 75.0

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

   11. Applied rewrites 75.0%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+39} \lor \neg \left(a \leq 8.5 \cdot 10^{+56}\right):\\ \;\;\;\;\mathsf{fma}\left(y, b, \left(1 - t\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + \left(\left(t + y\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+142} \lor \neg \left(b \leq 1.6 \cdot 10^{-20}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3e+142) (not (<= b 1.6e-20)))
   (fma (- (+ t y) 2.0) b a)
   (- x (fma (- t 1.0) a (- z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e+142) || !(b <= 1.6e-20)) {
		tmp = fma(((t + y) - 2.0), b, a);
	} else {
		tmp = x - fma((t - 1.0), a, -z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3e+142) || !(b <= 1.6e-20))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, a);
	else
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(-z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3e+142], N[Not[LessEqual[b, 1.6e-20]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + (-z)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.99999999999999975e142 or 1.59999999999999985e-20 < b

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 77.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 77.7

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

   7. Applied rewrites 77.7%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 83.8

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

   10. Applied rewrites 83.8%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 78.9%

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

   if -2.99999999999999975e142 < b < 1.59999999999999985e-20

   1. Initial program 95.4%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 97.4

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 67.4%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+142} \lor \neg \left(b \leq 1.6 \cdot 10^{-20}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, -z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-255}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right)\\ \mathbf{elif}\;y \leq 11.2:\\ \;\;\;\;x - \left(\left(-a\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3.6e+22)
     t_1
     (if (<= y 6.5e-255)
       (fma (- t 2.0) b x)
       (if (<= y 11.2) (- x (- (- a) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.6e+22) {
		tmp = t_1;
	} else if (y <= 6.5e-255) {
		tmp = fma((t - 2.0), b, x);
	} else if (y <= 11.2) {
		tmp = x - (-a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -3.6e+22)
		tmp = t_1;
	elseif (y <= 6.5e-255)
		tmp = fma(Float64(t - 2.0), b, x);
	elseif (y <= 11.2)
		tmp = Float64(x - Float64(Float64(-a) - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.6e+22], t$95$1, If[LessEqual[y, 6.5e-255], N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision], If[LessEqual[y, 11.2], N[(x - N[((-a) - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e22 or 11.199999999999999 < y

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 64.2

         \[\leadsto \left(b - z\right) \cdot y \]

   5. Applied rewrites 64.2%

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

   if -3.6e22 < y < 6.5e-255

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 55.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 55.0

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

   7. Applied rewrites 55.0%

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

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{t} - 2, b, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 54.3%

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

   if 6.5e-255 < y < 11.199999999999999

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 81.3%

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

   9. Taylor expanded in t around 0

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

       1. lower--.f64 N/A

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

       2. mul-1-neg N/A

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

       3. lift-neg.f64 59.9

          \[\leadsto x - \left(\left(-a\right) - z\right) \]

   11. Applied rewrites 59.9%

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

Alternative 13: 55.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -8 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-92}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 54000:\\ \;\;\;\;x - \left(\left(-a\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -8e+56)
     t_1
     (if (<= t -6e-92)
       (* (- b z) y)
       (if (<= t 54000.0) (- x (- (- a) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -8e+56) {
		tmp = t_1;
	} else if (t <= -6e-92) {
		tmp = (b - z) * y;
	} else if (t <= 54000.0) {
		tmp = x - (-a - z);
	} 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 = (b - a) * t
    if (t <= (-8d+56)) then
        tmp = t_1
    else if (t <= (-6d-92)) then
        tmp = (b - z) * y
    else if (t <= 54000.0d0) then
        tmp = x - (-a - z)
    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 = (b - a) * t;
	double tmp;
	if (t <= -8e+56) {
		tmp = t_1;
	} else if (t <= -6e-92) {
		tmp = (b - z) * y;
	} else if (t <= 54000.0) {
		tmp = x - (-a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -8e+56:
		tmp = t_1
	elif t <= -6e-92:
		tmp = (b - z) * y
	elif t <= 54000.0:
		tmp = x - (-a - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -8e+56)
		tmp = t_1;
	elseif (t <= -6e-92)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 54000.0)
		tmp = Float64(x - Float64(Float64(-a) - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -8e+56)
		tmp = t_1;
	elseif (t <= -6e-92)
		tmp = (b - z) * y;
	elseif (t <= 54000.0)
		tmp = x - (-a - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -8e+56], t$95$1, If[LessEqual[t, -6e-92], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 54000.0], N[(x - N[((-a) - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.00000000000000074e56 or 54000 < t

   1. Initial program 90.2%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 68.7

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

   5. Applied rewrites 68.7%

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

   if -8.00000000000000074e56 < t < -6.00000000000000027e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 59.4

         \[\leadsto \left(b - z\right) \cdot y \]

   5. Applied rewrites 59.4%

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

   if -6.00000000000000027e-92 < t < 54000

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 51.0%

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

   9. Taylor expanded in t around 0

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

       1. lower--.f64 N/A

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

       2. mul-1-neg N/A

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

       3. lift-neg.f64 50.4

          \[\leadsto x - \left(\left(-a\right) - z\right) \]

   11. Applied rewrites 50.4%

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

Alternative 14: 64.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+56} \lor \neg \left(b \leq 1.6 \cdot 10^{-20}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + \left(-y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.6e+56) (not (<= b 1.6e-20)))
   (fma (- (+ t y) 2.0) b a)
   (+ (+ x z) (* (- y) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.6e+56) || !(b <= 1.6e-20)) {
		tmp = fma(((t + y) - 2.0), b, a);
	} else {
		tmp = (x + z) + (-y * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.6e+56) || !(b <= 1.6e-20))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, a);
	else
		tmp = Float64(Float64(x + z) + Float64(Float64(-y) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.6e+56], N[Not[LessEqual[b, 1.6e-20]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + a), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[((-y) * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.60000000000000011e56 or 1.59999999999999985e-20 < b

   1. Initial program 91.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 72.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 72.6

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

   7. Applied rewrites 72.6%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 82.6

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

   10. Applied rewrites 82.6%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 75.3%

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

   if -2.60000000000000011e56 < b < 1.59999999999999985e-20

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 98.5

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in a around 0

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift--.f64 99.2

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

   8. Applied rewrites 99.2%

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

   9. Taylor expanded in z around inf

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

       1. mul-1-neg N/A

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

       2. distribute-lft-neg-out N/A

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

       3. lift-*.f64 N/A

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

       4. lift-neg.f64 57.7

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

   11. Applied rewrites 57.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+56} \lor \neg \left(b \leq 1.6 \cdot 10^{-20}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + \left(-y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+145} \lor \neg \left(a \leq 3.7 \cdot 10^{+124}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.4e+145) (not (<= a 3.7e+124)))
   (fma (- a) t a)
   (fma (- (+ t y) 2.0) b x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.4e+145) || !(a <= 3.7e+124)) {
		tmp = fma(-a, t, a);
	} else {
		tmp = fma(((t + y) - 2.0), b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.4e+145) || !(a <= 3.7e+124))
		tmp = fma(Float64(-a), t, a);
	else
		tmp = fma(Float64(Float64(t + y) - 2.0), b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.4e+145], N[Not[LessEqual[a, 3.7e+124]], $MachinePrecision]], N[((-a) * t + a), $MachinePrecision], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.39999999999999992e145 or 3.70000000000000008e124 < a

   1. Initial program 91.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), t, a\right) \]

      5. lift-neg.f64 71.6

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

   8. Applied rewrites 71.6%

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

   if -2.39999999999999992e145 < a < 3.70000000000000008e124

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 58.6%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 58.6

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

   7. Applied rewrites 58.6%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+145} \lor \neg \left(a \leq 3.7 \cdot 10^{+124}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+56} \lor \neg \left(t \leq 57000\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8e+56) (not (<= t 57000.0))) (* (- b a) t) (* (- b z) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8e+56) || !(t <= 57000.0)) {
		tmp = (b - a) * t;
	} else {
		tmp = (b - z) * y;
	}
	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 ((t <= (-8d+56)) .or. (.not. (t <= 57000.0d0))) then
        tmp = (b - a) * t
    else
        tmp = (b - z) * y
    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 ((t <= -8e+56) || !(t <= 57000.0)) {
		tmp = (b - a) * t;
	} else {
		tmp = (b - z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8e+56) or not (t <= 57000.0):
		tmp = (b - a) * t
	else:
		tmp = (b - z) * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8e+56) || !(t <= 57000.0))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(b - z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -8e+56) || ~((t <= 57000.0)))
		tmp = (b - a) * t;
	else
		tmp = (b - z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8e+56], N[Not[LessEqual[t, 57000.0]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.00000000000000074e56 or 57000 < t

   1. Initial program 90.2%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 68.7

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

   5. Applied rewrites 68.7%

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

   if -8.00000000000000074e56 < t < 57000

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 44.8

         \[\leadsto \left(b - z\right) \cdot y \]

   5. Applied rewrites 44.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+56} \lor \neg \left(t \leq 57000\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+31} \lor \neg \left(t \leq 57000\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.45e+31) (not (<= t 57000.0))) (* (- b a) t) (fma y b x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.45e+31) || !(t <= 57000.0)) {
		tmp = (b - a) * t;
	} else {
		tmp = fma(y, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.45e+31) || !(t <= 57000.0))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = fma(y, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.45e+31], N[Not[LessEqual[t, 57000.0]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(y * b + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e31 or 57000 < t

   1. Initial program 90.5%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 67.8

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

   5. Applied rewrites 67.8%

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

   if -1.45e31 < t < 57000

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 50.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 50.2

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

   7. Applied rewrites 50.2%

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

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 42.0%

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+31} \lor \neg \left(t \leq 57000\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+187} \lor \neg \left(t \leq 5.6 \cdot 10^{+92}\right):\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.3e+187) (not (<= t 5.6e+92))) (* (- a) t) (fma y b x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.3e+187) || !(t <= 5.6e+92)) {
		tmp = -a * t;
	} else {
		tmp = fma(y, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.3e+187) || !(t <= 5.6e+92))
		tmp = Float64(Float64(-a) * t);
	else
		tmp = fma(y, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.3e+187], N[Not[LessEqual[t, 5.6e+92]], $MachinePrecision]], N[((-a) * t), $MachinePrecision], N[(y * b + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.30000000000000004e187 or 5.60000000000000001e92 < t

   1. Initial program 88.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 79.7

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

   5. Applied rewrites 79.7%

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

   6. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 54.3

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

   8. Applied rewrites 54.3%

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

   if -2.30000000000000004e187 < t < 5.60000000000000001e92

   1. Initial program 97.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 51.4%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right) \]

      9. lower-+.f64 51.4

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right) \]

   7. Applied rewrites 51.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 39.9%

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+187} \lor \neg \left(t \leq 5.6 \cdot 10^{+92}\right):\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 41.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+22} \lor \neg \left(y \leq 1.15 \cdot 10^{+16}\right):\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.5e+22) (not (<= y 1.15e+16))) (fma y b x) (fma t b x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e+22) || !(y <= 1.15e+16)) {
		tmp = fma(y, b, x);
	} else {
		tmp = fma(t, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.5e+22) || !(y <= 1.15e+16))
		tmp = fma(y, b, x);
	else
		tmp = fma(t, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.5e+22], N[Not[LessEqual[y, 1.15e+16]], $MachinePrecision]], N[(y * b + x), $MachinePrecision], N[(t * b + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e22 or 1.15e16 < y

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

   5. Applied rewrites 50.2%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      3. lift-+.f64 N/A

         \[\leadsto x + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      4. lift--.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + x} \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)} \]

      7. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, x\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right) \]

      9. lower-+.f64 50.2

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right) \]

   7. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 45.9%

       \[\leadsto \mathsf{fma}\left(\color{blue}{y}, b, x\right) \]

   if -1.5e22 < y < 1.15e16

   1. Initial program 96.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

   5. Applied rewrites 47.2%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      3. lift-+.f64 N/A

         \[\leadsto x + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      4. lift--.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + x} \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)} \]

      7. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, x\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right) \]

      9. lower-+.f64 47.2

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right) \]

   7. Applied rewrites 47.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)} \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 37.0%

       \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+22} \lor \neg \left(y \leq 1.15 \cdot 10^{+16}\right):\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+23} \lor \neg \left(y \leq 1.52 \cdot 10^{+75}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e+23) (not (<= y 1.52e+75))) (* b y) (fma t b x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+23) || !(y <= 1.52e+75)) {
		tmp = b * y;
	} else {
		tmp = fma(t, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e+23) || !(y <= 1.52e+75))
		tmp = Float64(b * y);
	else
		tmp = fma(t, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e+23], N[Not[LessEqual[y, 1.52e+75]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(t * b + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e23 or 1.5199999999999999e75 < y

   1. Initial program 92.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 67.0

         \[\leadsto \left(b - z\right) \cdot y \]

   5. Applied rewrites 67.0%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   6. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 39.7%

      \[\leadsto b \cdot y \]

   if -1.15e23 < y < 1.5199999999999999e75

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

   5. Applied rewrites 45.0%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      3. lift-+.f64 N/A

         \[\leadsto x + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      4. lift--.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + x} \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)} \]

      7. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y + t\right) - 2}, b, x\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right) \]

      9. lower-+.f64 45.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right) \]

   7. Applied rewrites 45.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)} \]

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 34.4%

       \[\leadsto \mathsf{fma}\left(\color{blue}{t}, b, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+23} \lor \neg \left(y \leq 1.52 \cdot 10^{+75}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 36.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+25} \lor \neg \left(y \leq 850000000\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.5e+25) (not (<= y 850000000.0))) (* b y) (- x (- z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e+25) || !(y <= 850000000.0)) {
		tmp = b * y;
	} else {
		tmp = x - -z;
	}
	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 ((y <= (-1.5d+25)) .or. (.not. (y <= 850000000.0d0))) then
        tmp = b * y
    else
        tmp = x - -z
    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 ((y <= -1.5e+25) || !(y <= 850000000.0)) {
		tmp = b * y;
	} else {
		tmp = x - -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.5e+25) or not (y <= 850000000.0):
		tmp = b * y
	else:
		tmp = x - -z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.5e+25) || !(y <= 850000000.0))
		tmp = Float64(b * y);
	else
		tmp = Float64(x - Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.5e+25) || ~((y <= 850000000.0)))
		tmp = b * y;
	else
		tmp = x - -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.5e+25], N[Not[LessEqual[y, 850000000.0]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(x - (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000003e25 or 8.5e8 < y

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 65.6

         \[\leadsto \left(b - z\right) \cdot y \]

   5. Applied rewrites 65.6%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   6. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 36.3%

      \[\leadsto b \cdot y \]

   if -1.50000000000000003e25 < y < 8.5e8

   1. Initial program 96.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right) - \left(\color{blue}{-1 \cdot z} + a \cdot \left(t - 1\right)\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right) - \left(\color{blue}{-1 \cdot z} + a \cdot \left(t - 1\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \left(\left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right) + x\right) - \left(\color{blue}{-1} \cdot z + a \cdot \left(t - 1\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\left(\left(b - z\right) \cdot y + b \cdot \left(t - 2\right)\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(b - z, y, b \cdot \left(t - 2\right)\right) + x\right) - \left(\color{blue}{-1} \cdot z + a \cdot \left(t - 1\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(b - z, y, b \cdot \left(t - 2\right)\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      10. lower--.f64 N/A

          \[\leadsto \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \left(a \cdot \left(t - 1\right) + \color{blue}{-1 \cdot z}\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \left(\left(t - 1\right) \cdot a + \color{blue}{-1} \cdot z\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(t - 1, \color{blue}{a}, -1 \cdot z\right) \]

      14. lift--.f64 N/A

          \[\leadsto \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(t - 1, a, -1 \cdot z\right) \]

      15. mul-1-neg N/A

          \[\leadsto \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(t - 1, a, \mathsf{neg}\left(z\right)\right) \]

      16. lower-neg.f64 96.7

          \[\leadsto \left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(t - 1, a, -z\right) \]

   5. Applied rewrites 96.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right) + x\right) - \mathsf{fma}\left(t - 1, a, -z\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto x - \mathsf{fma}\left(\color{blue}{t - 1}, a, -z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 68.4%

      \[\leadsto x - \mathsf{fma}\left(\color{blue}{t - 1}, a, -z\right) \]

   9. Taylor expanded in z around inf

      \[\leadsto x - -1 \cdot \color{blue}{z} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x - \left(\mathsf{neg}\left(z\right)\right) \]

       2. lift-neg.f64 32.9

          \[\leadsto x - \left(-z\right) \]

   11. Applied rewrites 32.9%

       \[\leadsto x - \left(-z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+25} \lor \neg \left(y \leq 850000000\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 27.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+22} \lor \neg \left(y \leq 9.5 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.5e+22) (not (<= y 9.5e+14))) (* b y) (* b t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e+22) || !(y <= 9.5e+14)) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	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 ((y <= (-1.5d+22)) .or. (.not. (y <= 9.5d+14))) then
        tmp = b * y
    else
        tmp = b * t
    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 ((y <= -1.5e+22) || !(y <= 9.5e+14)) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.5e+22) or not (y <= 9.5e+14):
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.5e+22) || !(y <= 9.5e+14))
		tmp = Float64(b * y);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.5e+22) || ~((y <= 9.5e+14)))
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.5e+22], N[Not[LessEqual[y, 9.5e+14]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e22 or 9.5e14 < y

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. 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 65.1

         \[\leadsto \left(b - z\right) \cdot y \]

   5. Applied rewrites 65.1%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   6. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 36.3%

      \[\leadsto b \cdot y \]

   if -1.5e22 < y < 9.5e14

   1. Initial program 96.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 43.3

         \[\leadsto \left(b - a\right) \cdot t \]

   5. Applied rewrites 43.3%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 23.6%

      \[\leadsto b \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+22} \lor \neg \left(y \leq 9.5 \cdot 10^{+14}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 25.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+77} \lor \neg \left(b \leq 1.95 \cdot 10^{+20}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.1e+77) (not (<= b 1.95e+20))) (* b t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.1e+77) || !(b <= 1.95e+20)) {
		tmp = b * t;
	} 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 ((b <= (-1.1d+77)) .or. (.not. (b <= 1.95d+20))) then
        tmp = b * t
    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 ((b <= -1.1e+77) || !(b <= 1.95e+20)) {
		tmp = b * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.1e+77) or not (b <= 1.95e+20):
		tmp = b * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.1e+77) || !(b <= 1.95e+20))
		tmp = Float64(b * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.1e+77) || ~((b <= 1.95e+20)))
		tmp = b * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.1e+77], N[Not[LessEqual[b, 1.95e+20]], $MachinePrecision]], N[(b * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -1.1e77 or 1.95e20 < b

   1. Initial program 92.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. 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 37.2

         \[\leadsto \left(b - a\right) \cdot t \]

   5. Applied rewrites 37.2%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 30.1%

      \[\leadsto b \cdot t \]

   if -1.1e77 < b < 1.95e20

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Applied rewrites 19.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+77} \lor \neg \left(b \leq 1.95 \cdot 10^{+20}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+198}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.1e+198) a (if (<= a 7.2e+56) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.1e+198) {
		tmp = a;
	} else if (a <= 7.2e+56) {
		tmp = x;
	} else {
		tmp = a;
	}
	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 (a <= (-3.1d+198)) then
        tmp = a
    else if (a <= 7.2d+56) then
        tmp = x
    else
        tmp = a
    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 (a <= -3.1e+198) {
		tmp = a;
	} else if (a <= 7.2e+56) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.1e+198:
		tmp = a
	elif a <= 7.2e+56:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.1e+198)
		tmp = a;
	elseif (a <= 7.2e+56)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.1e+198)
		tmp = a;
	elseif (a <= 7.2e+56)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.1e+198], a, If[LessEqual[a, 7.2e+56], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -3.09999999999999975e198 or 7.19999999999999996e56 < a

   1. Initial program 92.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

      3. lower--.f64 70.9

         \[\leadsto \left(1 - t\right) \cdot a \]

   5. Applied rewrites 70.9%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto a \]
   7. Step-by-step derivation

   8. Applied rewrites 25.6%

      \[\leadsto a \]

   if -3.09999999999999975e198 < a < 7.19999999999999996e56

   1. Initial program 96.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Applied rewrites 17.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 15.8% accurate, 37.0× 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 94.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Applied rewrites 13.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025064 
(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)))