Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.9% → 92.9%

Time: 5.5s

Alternatives: 21

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

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)
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
    code = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)
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
    code = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{-1}{a - z} \cdot \left(y - z\right), x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{z - a} \cdot \left(x - t\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-302)
     (fma (- x t) (* (/ -1.0 (- a z)) (- y z)) x)
     (if (<= t_1 0.0)
       (- (+ t (* -1.0 (/ (* y (- t x)) z))) (* -1.0 (/ (* a (- t x)) z)))
       (- x (* (/ (- z y) (- z a)) (- x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-302) {
		tmp = fma((x - t), ((-1.0 / (a - z)) * (y - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = (t + (-1.0 * ((y * (t - x)) / z))) - (-1.0 * ((a * (t - x)) / z));
	} else {
		tmp = x - (((z - y) / (z - a)) * (x - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-302)
		tmp = fma(Float64(x - t), Float64(Float64(-1.0 / Float64(a - z)) * Float64(y - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t + Float64(-1.0 * Float64(Float64(y * Float64(t - x)) / z))) - Float64(-1.0 * Float64(Float64(a * Float64(t - x)) / z)));
	else
		tmp = Float64(x - Float64(Float64(Float64(z - y) / Float64(z - a)) * Float64(x - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-302], N[(N[(x - t), $MachinePrecision] * N[(N[(-1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(t + N[(-1.0 * N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-303

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. mult-flip N/A

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 83.6

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

   3. Applied rewrites 83.6%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.9%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 45.9

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

   4. Applied rewrites 45.9%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg-rev N/A

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

      9. mult-flip N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 N/A

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

      14. metadata-eval 83.6

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

   5. Applied rewrites 83.6%

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

   7. Applied rewrites 83.7%

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

Alternative 2: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{-1}{a - z} \cdot \left(y - z\right), x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{z - a} \cdot \left(x - t\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-302)
     (fma (- x t) (* (/ -1.0 (- a z)) (- y z)) x)
     (if (<= t_1 0.0)
       (+ t (* -1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
       (- x (* (/ (- z y) (- z a)) (- x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-302) {
		tmp = fma((x - t), ((-1.0 / (a - z)) * (y - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = x - (((z - y) / (z - a)) * (x - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-302)
		tmp = fma(Float64(x - t), Float64(Float64(-1.0 / Float64(a - z)) * Float64(y - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	else
		tmp = Float64(x - Float64(Float64(Float64(z - y) / Float64(z - a)) * Float64(x - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-302], N[(N[(x - t), $MachinePrecision] * N[(N[(-1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(-1.0 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-303

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. mult-flip N/A

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 83.6

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

   3. Applied rewrites 83.6%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.9%

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

   2. Taylor expanded in z around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.5

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

   4. Applied rewrites 46.5%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg-rev N/A

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

      9. mult-flip N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 N/A

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

      14. metadata-eval 83.6

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

   5. Applied rewrites 83.6%

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

   7. Applied rewrites 83.7%

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

Alternative 3: 86.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{-1}{a - z} \cdot \left(y - z\right), x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{z - a} \cdot \left(x - t\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-302)
     (fma (- x t) (* (/ -1.0 (- a z)) (- y z)) x)
     (if (<= t_1 5e-177)
       (* t (- (/ y (- a z)) (/ z (- a z))))
       (- x (* (/ (- z y) (- z a)) (- x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-302) {
		tmp = fma((x - t), ((-1.0 / (a - z)) * (y - z)), x);
	} else if (t_1 <= 5e-177) {
		tmp = t * ((y / (a - z)) - (z / (a - z)));
	} else {
		tmp = x - (((z - y) / (z - a)) * (x - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-302)
		tmp = fma(Float64(x - t), Float64(Float64(-1.0 / Float64(a - z)) * Float64(y - z)), x);
	elseif (t_1 <= 5e-177)
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) - Float64(z / Float64(a - z))));
	else
		tmp = Float64(x - Float64(Float64(Float64(z - y) / Float64(z - a)) * Float64(x - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-302], N[(N[(x - t), $MachinePrecision] * N[(N[(-1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5e-177], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-303

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. mult-flip N/A

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

      8. associate-*l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 83.6

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

   3. Applied rewrites 83.6%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e-177

   1. Initial program 79.9%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.5

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

   4. Applied rewrites 51.5%

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

   if 5e-177 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg-rev N/A

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

      9. mult-flip N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 N/A

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

      14. metadata-eval 83.6

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

   5. Applied rewrites 83.6%

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

   7. Applied rewrites 83.7%

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

Alternative 4: 86.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{z - y}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{z - a} \cdot \left(x - t\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-302)
     (fma (- x t) (/ (- z y) (- a z)) x)
     (if (<= t_1 5e-177)
       (* t (- (/ y (- a z)) (/ z (- a z))))
       (- x (* (/ (- z y) (- z a)) (- x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-302) {
		tmp = fma((x - t), ((z - y) / (a - z)), x);
	} else if (t_1 <= 5e-177) {
		tmp = t * ((y / (a - z)) - (z / (a - z)));
	} else {
		tmp = x - (((z - y) / (z - a)) * (x - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-302)
		tmp = fma(Float64(x - t), Float64(Float64(z - y) / Float64(a - z)), x);
	elseif (t_1 <= 5e-177)
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) - Float64(z / Float64(a - z))));
	else
		tmp = Float64(x - Float64(Float64(Float64(z - y) / Float64(z - a)) * Float64(x - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-302], N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5e-177], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-303

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e-177

   1. Initial program 79.9%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.5

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

   4. Applied rewrites 51.5%

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

   if 5e-177 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg-rev N/A

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

      9. mult-flip N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 N/A

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

      14. metadata-eval 83.6

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

   5. Applied rewrites 83.6%

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

   7. Applied rewrites 83.7%

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

Alternative 5: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{z - y}{a - z}, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-177}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{z - a} \cdot \left(x - t\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-302)
     (fma (- x t) (/ (- z y) (- a z)) x)
     (if (<= t_1 5e-177)
       (/ (* t (- y z)) (- a z))
       (- x (* (/ (- z y) (- z a)) (- x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-302) {
		tmp = fma((x - t), ((z - y) / (a - z)), x);
	} else if (t_1 <= 5e-177) {
		tmp = (t * (y - z)) / (a - z);
	} else {
		tmp = x - (((z - y) / (z - a)) * (x - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-302)
		tmp = fma(Float64(x - t), Float64(Float64(z - y) / Float64(a - z)), x);
	elseif (t_1 <= 5e-177)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	else
		tmp = Float64(x - Float64(Float64(Float64(z - y) / Float64(z - a)) * Float64(x - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-302], N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 5e-177], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-303

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e-177

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.7

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

   4. Applied rewrites 39.7%

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

   if 5e-177 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg-rev N/A

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

      9. mult-flip N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 N/A

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

      14. metadata-eval 83.6

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

   5. Applied rewrites 83.6%

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

   7. Applied rewrites 83.7%

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

Alternative 6: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{z - y}{a - z}, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-177}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x t) (/ (- z y) (- a z)) x))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-302)
     t_1
     (if (<= t_2 5e-177) (/ (* t (- y z)) (- a z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), ((z - y) / (a - z)), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-302) {
		tmp = t_1;
	} else if (t_2 <= 5e-177) {
		tmp = (t * (y - z)) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(Float64(z - y) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-302)
		tmp = t_1;
	elseif (t_2 <= 5e-177)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-302], t$95$1, If[LessEqual[t$95$2, 5e-177], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-303 or 5e-177 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e-177

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.7

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

   4. Applied rewrites 39.7%

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

Alternative 7: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{y}{z - a}, x\right)\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x t) (/ y (- z a)) x)))
   (if (<= y -5.4e+129)
     t_1
     (if (<= y 3.2e+78) (fma (/ (- y z) (- a z)) t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), (y / (z - a)), x);
	double tmp;
	if (y <= -5.4e+129) {
		tmp = t_1;
	} else if (y <= 3.2e+78) {
		tmp = fma(((y - z) / (a - z)), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(y / Float64(z - a)), x)
	tmp = 0.0
	if (y <= -5.4e+129)
		tmp = t_1;
	elseif (y <= 3.2e+78)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -5.4e+129], t$95$1, If[LessEqual[y, 3.2e+78], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4000000000000002e129 or 3.19999999999999994e78 < y

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg-rev N/A

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

      9. div-flip N/A

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

      10. metadata-eval N/A

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

      11. lower-unsound-/.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-unsound-/.f64 83.6

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

   5. Applied rewrites 83.6%

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

   6. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 60.8

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

   8. Applied rewrites 60.8%

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

   if -5.4000000000000002e129 < y < 3.19999999999999994e78

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 64.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. mult-flip-rev N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 67.2

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

   6. Applied rewrites 67.2%

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

Alternative 8: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{y}{z - a}, x\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-207}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{z}{a - z}, x\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{z - a}, z - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x t) (/ y (- z a)) x)))
   (if (<= y -5.2e-13)
     t_1
     (if (<= y 5.4e-207)
       (fma (- x t) (/ z (- a z)) x)
       (if (<= y 3.2e+78) (fma (/ t (- z a)) (- z y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), (y / (z - a)), x);
	double tmp;
	if (y <= -5.2e-13) {
		tmp = t_1;
	} else if (y <= 5.4e-207) {
		tmp = fma((x - t), (z / (a - z)), x);
	} else if (y <= 3.2e+78) {
		tmp = fma((t / (z - a)), (z - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(y / Float64(z - a)), x)
	tmp = 0.0
	if (y <= -5.2e-13)
		tmp = t_1;
	elseif (y <= 5.4e-207)
		tmp = fma(Float64(x - t), Float64(z / Float64(a - z)), x);
	elseif (y <= 3.2e+78)
		tmp = fma(Float64(t / Float64(z - a)), Float64(z - y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -5.2e-13], t$95$1, If[LessEqual[y, 5.4e-207], N[(N[(x - t), $MachinePrecision] * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 3.2e+78], N[(N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000001e-13 or 3.19999999999999994e78 < y

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg-rev N/A

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

      9. div-flip N/A

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

      10. metadata-eval N/A

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

      11. lower-unsound-/.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-unsound-/.f64 83.6

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

   5. Applied rewrites 83.6%

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

   6. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 60.8

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

   8. Applied rewrites 60.8%

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

   if -5.2000000000000001e-13 < y < 5.4e-207

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 46.4%

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

   if 5.4e-207 < y < 3.19999999999999994e78

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 64.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. distribute-rgt-neg-out N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. distribute-neg-frac2 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lift--.f64 N/A

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

      16. lower-/.f64 64.2

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

   6. Applied rewrites 64.2%

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

Alternative 9: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{y}{z - a}, x\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.76 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x t) (/ y (- z a)) x)))
   (if (<= y -5.2e-13)
     t_1
     (if (<= y 1.76e+78) (fma (- x t) (/ z (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), (y / (z - a)), x);
	double tmp;
	if (y <= -5.2e-13) {
		tmp = t_1;
	} else if (y <= 1.76e+78) {
		tmp = fma((x - t), (z / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(y / Float64(z - a)), x)
	tmp = 0.0
	if (y <= -5.2e-13)
		tmp = t_1;
	elseif (y <= 1.76e+78)
		tmp = fma(Float64(x - t), Float64(z / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -5.2e-13], t$95$1, If[LessEqual[y, 1.76e+78], N[(N[(x - t), $MachinePrecision] * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000001e-13 or 1.76e78 < y

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg-rev N/A

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

      9. div-flip N/A

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

      10. metadata-eval N/A

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

      11. lower-unsound-/.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-unsound-/.f64 83.6

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

   5. Applied rewrites 83.6%

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

   6. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 60.8

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

   8. Applied rewrites 60.8%

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

   if -5.2000000000000001e-13 < y < 1.76e78

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 46.4%

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

Alternative 10: 65.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{a}, y - z, x\right)\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{y - z}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) a) (- y z) x)))
   (if (<= a -9.2e+61)
     t_1
     (if (<= a 3.5e-33) (fma (- x t) (/ (- y z) z) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / a), (y - z), x);
	double tmp;
	if (a <= -9.2e+61) {
		tmp = t_1;
	} else if (a <= 3.5e-33) {
		tmp = fma((x - t), ((y - z) / z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / a), Float64(y - z), x)
	tmp = 0.0
	if (a <= -9.2e+61)
		tmp = t_1;
	elseif (a <= 3.5e-33)
		tmp = fma(Float64(x - t), Float64(Float64(y - z) / z), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -9.2e+61], t$95$1, If[LessEqual[a, 3.5e-33], N[(N[(x - t), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.1999999999999998e61 or 3.4999999999999999e-33 < a

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 80.0

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 80.0

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

   3. Applied rewrites 80.0%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. frac-2neg N/A

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

      7. mult-flip N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 79.9

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

   5. Applied rewrites 79.9%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 51.4

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

   8. Applied rewrites 51.4%

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

   if -9.1999999999999998e61 < a < 3.4999999999999999e-33

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. frac-2neg-rev N/A

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

      9. mult-flip N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 N/A

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

      14. metadata-eval 83.6

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

   5. Applied rewrites 83.6%

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

   6. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 38.7

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

   8. Applied rewrites 38.7%

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

Alternative 11: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{a}, y - z, x\right)\\ \mathbf{if}\;a \leq -2.45 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-296}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-68}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) a) (- y z) x)))
   (if (<= a -2.45e+60)
     t_1
     (if (<= a -6.8e-296)
       (/ (* t (- y z)) (- a z))
       (if (<= a 1.46e-68) (/ (* y (- x t)) (- z a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / a), (y - z), x);
	double tmp;
	if (a <= -2.45e+60) {
		tmp = t_1;
	} else if (a <= -6.8e-296) {
		tmp = (t * (y - z)) / (a - z);
	} else if (a <= 1.46e-68) {
		tmp = (y * (x - t)) / (z - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / a), Float64(y - z), x)
	tmp = 0.0
	if (a <= -2.45e+60)
		tmp = t_1;
	elseif (a <= -6.8e-296)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	elseif (a <= 1.46e-68)
		tmp = Float64(Float64(y * Float64(x - t)) / Float64(z - a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.45e+60], t$95$1, If[LessEqual[a, -6.8e-296], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.46e-68], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4500000000000001e60 or 1.45999999999999998e-68 < a

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 80.0

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower--.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 80.0

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

   3. Applied rewrites 80.0%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-negate-rev N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. frac-2neg N/A

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

      7. mult-flip N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. frac-2neg N/A

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

      11. metadata-eval N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 79.9

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

   5. Applied rewrites 79.9%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 51.4

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

   8. Applied rewrites 51.4%

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

   if -2.4500000000000001e60 < a < -6.79999999999999993e-296

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.7

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

   4. Applied rewrites 39.7%

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

   if -6.79999999999999993e-296 < a < 1.45999999999999998e-68

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. frac-2neg N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. distribute-lft-neg-out N/A

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

      18. distribute-rgt-neg-out N/A

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

      19. lower-*.f64 N/A

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

      20. lower--.f64 N/A

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower--.f64 68.1

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

   3. Applied rewrites 68.1%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 38.5

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

   6. Applied rewrites 38.5%

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

Alternative 12: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-296}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+86}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a (- y z))))))
   (if (<= a -2e+60)
     t_1
     (if (<= a -6.8e-296)
       (/ (* t (- y z)) (- a z))
       (if (<= a 6.5e-67)
         (/ (* y (- x t)) (- z a))
         (if (<= a 3.2e+86) (+ x (* (- t x) (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / (y - z)));
	double tmp;
	if (a <= -2e+60) {
		tmp = t_1;
	} else if (a <= -6.8e-296) {
		tmp = (t * (y - z)) / (a - z);
	} else if (a <= 6.5e-67) {
		tmp = (y * (x - t)) / (z - a);
	} else if (a <= 3.2e+86) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / (y - z)))
    if (a <= (-2d+60)) then
        tmp = t_1
    else if (a <= (-6.8d-296)) then
        tmp = (t * (y - z)) / (a - z)
    else if (a <= 6.5d-67) then
        tmp = (y * (x - t)) / (z - a)
    else if (a <= 3.2d+86) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / (y - z)));
	double tmp;
	if (a <= -2e+60) {
		tmp = t_1;
	} else if (a <= -6.8e-296) {
		tmp = (t * (y - z)) / (a - z);
	} else if (a <= 6.5e-67) {
		tmp = (y * (x - t)) / (z - a);
	} else if (a <= 3.2e+86) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / (y - z)))
	tmp = 0
	if a <= -2e+60:
		tmp = t_1
	elif a <= -6.8e-296:
		tmp = (t * (y - z)) / (a - z)
	elif a <= 6.5e-67:
		tmp = (y * (x - t)) / (z - a)
	elif a <= 3.2e+86:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -2e+60)
		tmp = t_1;
	elseif (a <= -6.8e-296)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	elseif (a <= 6.5e-67)
		tmp = Float64(Float64(y * Float64(x - t)) / Float64(z - a));
	elseif (a <= 3.2e+86)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / (y - z)));
	tmp = 0.0;
	if (a <= -2e+60)
		tmp = t_1;
	elseif (a <= -6.8e-296)
		tmp = (t * (y - z)) / (a - z);
	elseif (a <= 6.5e-67)
		tmp = (y * (x - t)) / (z - a);
	elseif (a <= 3.2e+86)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+60], t$95$1, If[LessEqual[a, -6.8e-296], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-67], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+86], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9999999999999999e60 or 3.2e86 < a

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 64.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. div-flip N/A

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

      9. metadata-eval N/A

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

      10. lower-unsound-/.f64 N/A

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

      11. metadata-eval N/A

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

      12. lower-unsound-/.f64 N/A

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

      13. *-commutative N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. lower-*.f64 55.8

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

   6. Applied rewrites 55.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lift-/.f64 N/A

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

      11. div-flip-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lift-/.f64 N/A

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

      14. distribute-neg-frac N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 67.2

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

   8. Applied rewrites 67.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 45.2%

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

   if -1.9999999999999999e60 < a < -6.79999999999999993e-296

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.7

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

   4. Applied rewrites 39.7%

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

   if -6.79999999999999993e-296 < a < 6.4999999999999997e-67

   1. Initial program 79.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. frac-2neg N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. distribute-lft-neg-out N/A

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

      18. distribute-rgt-neg-out N/A

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

      19. lower-*.f64 N/A

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

      20. lower--.f64 N/A

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower--.f64 68.1

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

   3. Applied rewrites 68.1%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 38.5

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

   6. Applied rewrites 38.5%

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

   if 6.4999999999999997e-67 < a < 3.2e86

   1. Initial program 79.9%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.7

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

   4. Applied rewrites 43.7%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. mult-flip-rev N/A

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

      8. lower-/.f64 48.0

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

   6. Applied rewrites 48.0%

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

Alternative 13: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+60}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-296}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e+60)
   (fma (/ t a) (- y z) x)
   (if (<= a -6.8e-296)
     (/ (* t (- y z)) (- a z))
     (if (<= a 6.5e-67) (/ (* y (- x t)) (- z a)) (+ x (* (- t x) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+60) {
		tmp = fma((t / a), (y - z), x);
	} else if (a <= -6.8e-296) {
		tmp = (t * (y - z)) / (a - z);
	} else if (a <= 6.5e-67) {
		tmp = (y * (x - t)) / (z - a);
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e+60)
		tmp = fma(Float64(t / a), Float64(y - z), x);
	elseif (a <= -6.8e-296)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	elseif (a <= 6.5e-67)
		tmp = Float64(Float64(y * Float64(x - t)) / Float64(z - a));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e+60], N[(N[(t / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, -6.8e-296], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-67], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.9999999999999999e60

   1. Initial program 79.9%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 64.2%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 44.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 44.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)} \]

   9. Applied rewrites 44.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)} \]

   if -1.9999999999999999e60 < a < -6.79999999999999993e-296

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot \left(y - z\right)}{\color{blue}{a - z}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t \cdot \left(y - z\right)}{\color{blue}{a} - z} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{t \cdot \left(y - z\right)}{a - z} \]

      4. lower--.f64 39.7

         \[\leadsto \frac{t \cdot \left(y - z\right)}{a - \color{blue}{z}} \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   if -6.79999999999999993e-296 < a < 6.4999999999999997e-67

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x \]

      4. lift-/.f64 N/A

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}} + x \]

      5. mult-flip N/A

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} + x \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} + x \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - z}, \left(y - z\right) \cdot \left(t - x\right), x\right)} \]

      9. frac-2neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      13. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(y - z\right)} \cdot \left(t - x\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right), x\right) \]

      17. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)}, x\right) \]

      18. distribute-rgt-neg-out N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}, x\right) \]

      19. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}, x\right) \]

      20. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right), x\right) \]

      21. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right), x\right) \]

      22. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \color{blue}{\left(x - t\right)}, x\right) \]

      23. lower--.f64 68.1

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \color{blue}{\left(x - t\right)}, x\right) \]

   3. Applied rewrites 68.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \left(x - t\right), x\right)} \]

   4. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z - a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z} - a} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - a} \]

      4. lower--.f64 38.5

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - \color{blue}{a}} \]

   6. Applied rewrites 38.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]

   if 6.4999999999999997e-67 < a

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{\color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{a} \]

      3. lower--.f64 43.7

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{a} \]

   4. Applied rewrites 43.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{\color{blue}{a}} \]

      2. mult-flip N/A

         \[\leadsto x + \left(y \cdot \left(t - x\right)\right) \cdot \color{blue}{\frac{1}{a}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \left(y \cdot \left(t - x\right)\right) \cdot \frac{\color{blue}{1}}{a} \]

      4. *-commutative N/A

         \[\leadsto x + \left(\left(t - x\right) \cdot y\right) \cdot \frac{\color{blue}{1}}{a} \]

      5. associate-*l* N/A

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\left(y \cdot \frac{1}{a}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\left(y \cdot \frac{1}{a}\right)} \]

      7. mult-flip-rev N/A

         \[\leadsto x + \left(t - x\right) \cdot \frac{y}{\color{blue}{a}} \]

      8. lower-/.f64 48.0

         \[\leadsto x + \left(t - x\right) \cdot \frac{y}{\color{blue}{a}} \]

   6. Applied rewrites 48.0%

      \[\leadsto x + \left(t - x\right) \cdot \color{blue}{\frac{y}{a}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a}, y - z, x\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-296}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t a) (- y z) x)))
   (if (<= a -2e+60)
     t_1
     (if (<= a -6.8e-296)
       (/ (* t (- y z)) (- a z))
       (if (<= a 1.2e-16) (/ (* y (- x t)) (- z a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / a), (y - z), x);
	double tmp;
	if (a <= -2e+60) {
		tmp = t_1;
	} else if (a <= -6.8e-296) {
		tmp = (t * (y - z)) / (a - z);
	} else if (a <= 1.2e-16) {
		tmp = (y * (x - t)) / (z - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / a), Float64(y - z), x)
	tmp = 0.0
	if (a <= -2e+60)
		tmp = t_1;
	elseif (a <= -6.8e-296)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	elseif (a <= 1.2e-16)
		tmp = Float64(Float64(y * Float64(x - t)) / Float64(z - a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2e+60], t$95$1, If[LessEqual[a, -6.8e-296], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-16], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9999999999999999e60 or 1.20000000000000002e-16 < a

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]

   5. Taylor expanded in z around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{t}{\color{blue}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 44.1%

      \[\leadsto x + \left(y - z\right) \cdot \frac{t}{\color{blue}{a}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t}{a}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a} + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a}} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(y - z\right)} + x \]

      5. lower-fma.f64 44.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)} \]

   9. Applied rewrites 44.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)} \]

   if -1.9999999999999999e60 < a < -6.79999999999999993e-296

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot \left(y - z\right)}{\color{blue}{a - z}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t \cdot \left(y - z\right)}{\color{blue}{a} - z} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{t \cdot \left(y - z\right)}{a - z} \]

      4. lower--.f64 39.7

         \[\leadsto \frac{t \cdot \left(y - z\right)}{a - \color{blue}{z}} \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   if -6.79999999999999993e-296 < a < 1.20000000000000002e-16

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x \]

      4. lift-/.f64 N/A

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}} + x \]

      5. mult-flip N/A

         \[\leadsto \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} + x \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} + x \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} + x \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - z}, \left(y - z\right) \cdot \left(t - x\right), x\right)} \]

      9. frac-2neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      13. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{z - a}}, \left(y - z\right) \cdot \left(t - x\right), x\right) \]

      15. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(y - z\right)} \cdot \left(t - x\right), x\right) \]

      16. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right), x\right) \]

      17. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)}, x\right) \]

      18. distribute-rgt-neg-out N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}, x\right) \]

      19. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}, x\right) \]

      20. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right), x\right) \]

      21. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right), x\right) \]

      22. sub-negate-rev N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \color{blue}{\left(x - t\right)}, x\right) \]

      23. lower--.f64 68.1

          \[\leadsto \mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \color{blue}{\left(x - t\right)}, x\right) \]

   3. Applied rewrites 68.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{z - a}, \left(z - y\right) \cdot \left(x - t\right), x\right)} \]

   4. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z - a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{\color{blue}{z} - a} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - a} \]

      4. lower--.f64 38.5

         \[\leadsto \frac{y \cdot \left(x - t\right)}{z - \color{blue}{a}} \]

   6. Applied rewrites 38.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(x - t\right)}{z - a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 56.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a}, y - z, x\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-90}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t a) (- y z) x)))
   (if (<= a -2e+60) t_1 (if (<= a 5.6e-90) (/ (* t (- y z)) (- a z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / a), (y - z), x);
	double tmp;
	if (a <= -2e+60) {
		tmp = t_1;
	} else if (a <= 5.6e-90) {
		tmp = (t * (y - z)) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / a), Float64(y - z), x)
	tmp = 0.0
	if (a <= -2e+60)
		tmp = t_1;
	elseif (a <= 5.6e-90)
		tmp = Float64(Float64(t * Float64(y - z)) / Float64(a - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2e+60], t$95$1, If[LessEqual[a, 5.6e-90], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9999999999999999e60 or 5.5999999999999998e-90 < a

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]

   5. Taylor expanded in z around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{t}{\color{blue}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 44.1%

      \[\leadsto x + \left(y - z\right) \cdot \frac{t}{\color{blue}{a}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t}{a}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a} + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a}} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(y - z\right)} + x \]

      5. lower-fma.f64 44.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)} \]

   9. Applied rewrites 44.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)} \]

   if -1.9999999999999999e60 < a < 5.5999999999999998e-90

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot \left(y - z\right)}{\color{blue}{a - z}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t \cdot \left(y - z\right)}{\color{blue}{a} - z} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{t \cdot \left(y - z\right)}{a - z} \]

      4. lower--.f64 39.7

         \[\leadsto \frac{t \cdot \left(y - z\right)}{a - \color{blue}{z}} \]

   4. Applied rewrites 39.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 50.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55:\\ \;\;\;\;x + \frac{t}{1}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55)
   (+ x (/ t 1.0))
   (if (<= z 4.5e+129) (fma (/ t a) (- y z) x) (+ x (- t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55) {
		tmp = x + (t / 1.0);
	} else if (z <= 4.5e+129) {
		tmp = fma((t / a), (y - z), x);
	} else {
		tmp = x + (t - x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55)
		tmp = Float64(x + Float64(t / 1.0));
	elseif (z <= 4.5e+129)
		tmp = fma(Float64(t / a), Float64(y - z), x);
	else
		tmp = Float64(x + Float64(t - x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55], N[(x + N[(t / 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+129], N[(N[(t / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000004

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} \]

      3. associate-*r/ N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{a - z}} \]

      4. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \]

      5. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \]

      6. sub-negate-rev N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

      7. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

      8. div-flip N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      9. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

      10. lower-unsound-/.f64 N/A

          \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(-1\right)}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      11. metadata-eval N/A

          \[\leadsto x + \frac{\color{blue}{1}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

      12. lower-unsound-/.f64 N/A

          \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      13. *-commutative N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{\mathsf{neg}\left(\color{blue}{t \cdot \left(y - z\right)}\right)}} \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}}} \]

      15. lift--.f64 N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right)}} \]

      16. sub-negate-rev N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

      17. lift--.f64 N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

      18. lower-*.f64 55.8

          \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

   6. Applied rewrites 55.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

      4. *-commutative N/A

         \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{\left(z - y\right) \cdot t}}} \]

      5. associate-/r* N/A

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{z - y}}{t}}} \]

      6. lift--.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{z - y}}}{t}} \]

      7. sub-negate-rev N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{\mathsf{neg}\left(\left(y - z\right)\right)}}}{t}} \]

      8. lift--.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)}}{t}} \]

      9. distribute-neg-frac2 N/A

         \[\leadsto x + \frac{1}{\frac{\color{blue}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}}{t}} \]

      10. lift-/.f64 N/A

          \[\leadsto x + \frac{1}{\frac{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)}{t}} \]

      11. div-flip-rev N/A

          \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

      12. lower-/.f64 N/A

          \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

      13. lift-/.f64 N/A

          \[\leadsto x + \frac{t}{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)} \]

      14. distribute-neg-frac N/A

          \[\leadsto x + \frac{t}{\color{blue}{\frac{\mathsf{neg}\left(\left(z - a\right)\right)}{y - z}}} \]

      15. lift--.f64 N/A

          \[\leadsto x + \frac{t}{\frac{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)}{y - z}} \]

      16. sub-negate-rev N/A

          \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

      17. lower-/.f64 N/A

          \[\leadsto x + \frac{t}{\color{blue}{\frac{a - z}{y - z}}} \]

      18. lower--.f64 67.2

          \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

   8. Applied rewrites 67.2%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   9. Taylor expanded in z around inf

      \[\leadsto x + \frac{t}{\color{blue}{1}} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.3%

       \[\leadsto x + \frac{t}{\color{blue}{1}} \]

   if -1.55000000000000004 < z < 4.5000000000000001e129

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]

   5. Taylor expanded in z around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{t}{\color{blue}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 44.1%

      \[\leadsto x + \left(y - z\right) \cdot \frac{t}{\color{blue}{a}} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t}{a}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a} + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t}{a}} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(y - z\right)} + x \]

      5. lower-fma.f64 44.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)} \]

   9. Applied rewrites 44.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)} \]

   if 4.5000000000000001e129 < z

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.1

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.1%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 49.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{t}{1}\\ \mathbf{if}\;z \leq -8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t 1.0))))
   (if (<= z -8.0) t_1 (if (<= z 1.25e+78) (+ x (/ t (/ a y))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / 1.0);
	double tmp;
	if (z <= -8.0) {
		tmp = t_1;
	} else if (z <= 1.25e+78) {
		tmp = x + (t / (a / y));
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (t / 1.0d0)
    if (z <= (-8.0d0)) then
        tmp = t_1
    else if (z <= 1.25d+78) then
        tmp = x + (t / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / 1.0);
	double tmp;
	if (z <= -8.0) {
		tmp = t_1;
	} else if (z <= 1.25e+78) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / 1.0)
	tmp = 0
	if z <= -8.0:
		tmp = t_1
	elif z <= 1.25e+78:
		tmp = x + (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / 1.0))
	tmp = 0.0
	if (z <= -8.0)
		tmp = t_1;
	elseif (z <= 1.25e+78)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / 1.0);
	tmp = 0.0;
	if (z <= -8.0)
		tmp = t_1;
	elseif (z <= 1.25e+78)
		tmp = x + (t / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.0], t$95$1, If[LessEqual[z, 1.25e+78], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8 or 1.24999999999999996e78 < z

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} \]

      3. associate-*r/ N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{a - z}} \]

      4. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \]

      5. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \]

      6. sub-negate-rev N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

      7. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

      8. div-flip N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      9. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

      10. lower-unsound-/.f64 N/A

          \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(-1\right)}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      11. metadata-eval N/A

          \[\leadsto x + \frac{\color{blue}{1}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

      12. lower-unsound-/.f64 N/A

          \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      13. *-commutative N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{\mathsf{neg}\left(\color{blue}{t \cdot \left(y - z\right)}\right)}} \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}}} \]

      15. lift--.f64 N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right)}} \]

      16. sub-negate-rev N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

      17. lift--.f64 N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

      18. lower-*.f64 55.8

          \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

   6. Applied rewrites 55.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

      4. *-commutative N/A

         \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{\left(z - y\right) \cdot t}}} \]

      5. associate-/r* N/A

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{z - y}}{t}}} \]

      6. lift--.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{z - y}}}{t}} \]

      7. sub-negate-rev N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{\mathsf{neg}\left(\left(y - z\right)\right)}}}{t}} \]

      8. lift--.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)}}{t}} \]

      9. distribute-neg-frac2 N/A

         \[\leadsto x + \frac{1}{\frac{\color{blue}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}}{t}} \]

      10. lift-/.f64 N/A

          \[\leadsto x + \frac{1}{\frac{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)}{t}} \]

      11. div-flip-rev N/A

          \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

      12. lower-/.f64 N/A

          \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

      13. lift-/.f64 N/A

          \[\leadsto x + \frac{t}{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)} \]

      14. distribute-neg-frac N/A

          \[\leadsto x + \frac{t}{\color{blue}{\frac{\mathsf{neg}\left(\left(z - a\right)\right)}{y - z}}} \]

      15. lift--.f64 N/A

          \[\leadsto x + \frac{t}{\frac{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)}{y - z}} \]

      16. sub-negate-rev N/A

          \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

      17. lower-/.f64 N/A

          \[\leadsto x + \frac{t}{\color{blue}{\frac{a - z}{y - z}}} \]

      18. lower--.f64 67.2

          \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

   8. Applied rewrites 67.2%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   9. Taylor expanded in z around inf

      \[\leadsto x + \frac{t}{\color{blue}{1}} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.3%

       \[\leadsto x + \frac{t}{\color{blue}{1}} \]

   if -8 < z < 1.24999999999999996e78

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} \]

      3. associate-*r/ N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{a - z}} \]

      4. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \]

      5. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \]

      6. sub-negate-rev N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

      7. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

      8. div-flip N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      9. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

      10. lower-unsound-/.f64 N/A

          \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(-1\right)}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      11. metadata-eval N/A

          \[\leadsto x + \frac{\color{blue}{1}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

      12. lower-unsound-/.f64 N/A

          \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      13. *-commutative N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{\mathsf{neg}\left(\color{blue}{t \cdot \left(y - z\right)}\right)}} \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}}} \]

      15. lift--.f64 N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right)}} \]

      16. sub-negate-rev N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

      17. lift--.f64 N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

      18. lower-*.f64 55.8

          \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

   6. Applied rewrites 55.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

      4. *-commutative N/A

         \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{\left(z - y\right) \cdot t}}} \]

      5. associate-/r* N/A

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{z - y}}{t}}} \]

      6. lift--.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{z - y}}}{t}} \]

      7. sub-negate-rev N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{\mathsf{neg}\left(\left(y - z\right)\right)}}}{t}} \]

      8. lift--.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)}}{t}} \]

      9. distribute-neg-frac2 N/A

         \[\leadsto x + \frac{1}{\frac{\color{blue}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}}{t}} \]

      10. lift-/.f64 N/A

          \[\leadsto x + \frac{1}{\frac{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)}{t}} \]

      11. div-flip-rev N/A

          \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

      12. lower-/.f64 N/A

          \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

      13. lift-/.f64 N/A

          \[\leadsto x + \frac{t}{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)} \]

      14. distribute-neg-frac N/A

          \[\leadsto x + \frac{t}{\color{blue}{\frac{\mathsf{neg}\left(\left(z - a\right)\right)}{y - z}}} \]

      15. lift--.f64 N/A

          \[\leadsto x + \frac{t}{\frac{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)}{y - z}} \]

      16. sub-negate-rev N/A

          \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

      17. lower-/.f64 N/A

          \[\leadsto x + \frac{t}{\color{blue}{\frac{a - z}{y - z}}} \]

      18. lower--.f64 67.2

          \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

   8. Applied rewrites 67.2%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   9. Taylor expanded in z around 0

      \[\leadsto x + \frac{t}{\color{blue}{\frac{a}{y}}} \]
   10. Step-by-step derivation

       1. lower-/.f64 40.7

          \[\leadsto x + \frac{t}{\frac{a}{\color{blue}{y}}} \]

   11. Applied rewrites 40.7%

       \[\leadsto x + \frac{t}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 47.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{t}{1}\\ \mathbf{if}\;z \leq -8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t 1.0))))
   (if (<= z -8.0) t_1 (if (<= z 2.05e+77) (+ x (/ (* t y) a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / 1.0);
	double tmp;
	if (z <= -8.0) {
		tmp = t_1;
	} else if (z <= 2.05e+77) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (t / 1.0d0)
    if (z <= (-8.0d0)) then
        tmp = t_1
    else if (z <= 2.05d+77) then
        tmp = x + ((t * y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / 1.0);
	double tmp;
	if (z <= -8.0) {
		tmp = t_1;
	} else if (z <= 2.05e+77) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / 1.0)
	tmp = 0
	if z <= -8.0:
		tmp = t_1
	elif z <= 2.05e+77:
		tmp = x + ((t * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / 1.0))
	tmp = 0.0
	if (z <= -8.0)
		tmp = t_1;
	elseif (z <= 2.05e+77)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / 1.0);
	tmp = 0.0;
	if (z <= -8.0)
		tmp = t_1;
	elseif (z <= 2.05e+77)
		tmp = x + ((t * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.0], t$95$1, If[LessEqual[z, 2.05e+77], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8 or 2.05e77 < z

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in x around 0

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.2%

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} \]

      3. associate-*r/ N/A

         \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{a - z}} \]

      4. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \]

      5. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \]

      6. sub-negate-rev N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

      7. lift--.f64 N/A

         \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

      8. div-flip N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      9. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

      10. lower-unsound-/.f64 N/A

          \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(-1\right)}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      11. metadata-eval N/A

          \[\leadsto x + \frac{\color{blue}{1}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

      12. lower-unsound-/.f64 N/A

          \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

      13. *-commutative N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{\mathsf{neg}\left(\color{blue}{t \cdot \left(y - z\right)}\right)}} \]

      14. distribute-rgt-neg-in N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}}} \]

      15. lift--.f64 N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right)}} \]

      16. sub-negate-rev N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

      17. lift--.f64 N/A

          \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

      18. lower-*.f64 55.8

          \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

   6. Applied rewrites 55.8%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

      4. *-commutative N/A

         \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{\left(z - y\right) \cdot t}}} \]

      5. associate-/r* N/A

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{z - y}}{t}}} \]

      6. lift--.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{z - y}}}{t}} \]

      7. sub-negate-rev N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{\mathsf{neg}\left(\left(y - z\right)\right)}}}{t}} \]

      8. lift--.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)}}{t}} \]

      9. distribute-neg-frac2 N/A

         \[\leadsto x + \frac{1}{\frac{\color{blue}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}}{t}} \]

      10. lift-/.f64 N/A

          \[\leadsto x + \frac{1}{\frac{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)}{t}} \]

      11. div-flip-rev N/A

          \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

      12. lower-/.f64 N/A

          \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

      13. lift-/.f64 N/A

          \[\leadsto x + \frac{t}{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)} \]

      14. distribute-neg-frac N/A

          \[\leadsto x + \frac{t}{\color{blue}{\frac{\mathsf{neg}\left(\left(z - a\right)\right)}{y - z}}} \]

      15. lift--.f64 N/A

          \[\leadsto x + \frac{t}{\frac{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)}{y - z}} \]

      16. sub-negate-rev N/A

          \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

      17. lower-/.f64 N/A

          \[\leadsto x + \frac{t}{\color{blue}{\frac{a - z}{y - z}}} \]

      18. lower--.f64 67.2

          \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

   8. Applied rewrites 67.2%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   9. Taylor expanded in z around inf

      \[\leadsto x + \frac{t}{\color{blue}{1}} \]
   10. Step-by-step derivation

   11. Applied rewrites 33.3%

       \[\leadsto x + \frac{t}{\color{blue}{1}} \]

   if -8 < z < 2.05e77

   1. Initial program 79.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{\color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{a} \]

      3. lower--.f64 43.7

         \[\leadsto x + \frac{y \cdot \left(t - x\right)}{a} \]

   4. Applied rewrites 43.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + \frac{t \cdot y}{a} \]
   6. Step-by-step derivation

      1. lower-*.f64 38.0

         \[\leadsto x + \frac{t \cdot y}{a} \]

   7. Applied rewrites 38.0%

      \[\leadsto x + \frac{t \cdot y}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 33.3% accurate, 2.5× speedup

Math

\[x + \frac{t}{1} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ t 1.0)))

C

double code(double x, double y, double z, double t, double a) {
	return x + (t / 1.0);
}

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)
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
    code = x + (t / 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (t / 1.0);
}

Python

def code(x, y, z, t, a):
	return x + (t / 1.0)

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(t / 1.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (t / 1.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(t / 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

2. Taylor expanded in x around 0

   \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
3. Step-by-step derivation

4. Applied rewrites 64.2%

   \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{t}}{a - z} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t}{a - z}} \]

   2. lift-/.f64 N/A

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}} \]

   3. associate-*r/ N/A

      \[\leadsto x + \color{blue}{\frac{\left(y - z\right) \cdot t}{a - z}} \]

   4. frac-2neg N/A

      \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \]

   5. lift--.f64 N/A

      \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \]

   6. sub-negate-rev N/A

      \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

   7. lift--.f64 N/A

      \[\leadsto x + \frac{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}{\color{blue}{z - a}} \]

   8. div-flip N/A

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

   9. metadata-eval N/A

      \[\leadsto x + \frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

   10. lower-unsound-/.f64 N/A

       \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(-1\right)}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

   11. metadata-eval N/A

       \[\leadsto x + \frac{\color{blue}{1}}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}} \]

   12. lower-unsound-/.f64 N/A

       \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{\mathsf{neg}\left(\left(y - z\right) \cdot t\right)}}} \]

   13. *-commutative N/A

       \[\leadsto x + \frac{1}{\frac{z - a}{\mathsf{neg}\left(\color{blue}{t \cdot \left(y - z\right)}\right)}} \]

   14. distribute-rgt-neg-in N/A

       \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}}} \]

   15. lift--.f64 N/A

       \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right)}} \]

   16. sub-negate-rev N/A

       \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

   17. lift--.f64 N/A

       \[\leadsto x + \frac{1}{\frac{z - a}{t \cdot \color{blue}{\left(z - y\right)}}} \]

   18. lower-*.f64 55.8

       \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

6. Applied rewrites 55.8%

   \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]
7. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

   2. lift-/.f64 N/A

      \[\leadsto x + \frac{1}{\color{blue}{\frac{z - a}{t \cdot \left(z - y\right)}}} \]

   3. lift-*.f64 N/A

      \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{t \cdot \left(z - y\right)}}} \]

   4. *-commutative N/A

      \[\leadsto x + \frac{1}{\frac{z - a}{\color{blue}{\left(z - y\right) \cdot t}}} \]

   5. associate-/r* N/A

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{z - a}{z - y}}{t}}} \]

   6. lift--.f64 N/A

      \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{z - y}}}{t}} \]

   7. sub-negate-rev N/A

      \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\color{blue}{\mathsf{neg}\left(\left(y - z\right)\right)}}}{t}} \]

   8. lift--.f64 N/A

      \[\leadsto x + \frac{1}{\frac{\frac{z - a}{\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)}}{t}} \]

   9. distribute-neg-frac2 N/A

      \[\leadsto x + \frac{1}{\frac{\color{blue}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}}{t}} \]

   10. lift-/.f64 N/A

       \[\leadsto x + \frac{1}{\frac{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)}{t}} \]

   11. div-flip-rev N/A

       \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

   12. lower-/.f64 N/A

       \[\leadsto x + \color{blue}{\frac{t}{\mathsf{neg}\left(\frac{z - a}{y - z}\right)}} \]

   13. lift-/.f64 N/A

       \[\leadsto x + \frac{t}{\mathsf{neg}\left(\color{blue}{\frac{z - a}{y - z}}\right)} \]

   14. distribute-neg-frac N/A

       \[\leadsto x + \frac{t}{\color{blue}{\frac{\mathsf{neg}\left(\left(z - a\right)\right)}{y - z}}} \]

   15. lift--.f64 N/A

       \[\leadsto x + \frac{t}{\frac{\mathsf{neg}\left(\color{blue}{\left(z - a\right)}\right)}{y - z}} \]

   16. sub-negate-rev N/A

       \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

   17. lower-/.f64 N/A

       \[\leadsto x + \frac{t}{\color{blue}{\frac{a - z}{y - z}}} \]

   18. lower--.f64 67.2

       \[\leadsto x + \frac{t}{\frac{\color{blue}{a - z}}{y - z}} \]

8. Applied rewrites 67.2%

   \[\leadsto x + \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

9. Taylor expanded in z around inf

   \[\leadsto x + \frac{t}{\color{blue}{1}} \]
10. Step-by-step derivation

11. Applied rewrites 33.3%

    \[\leadsto x + \frac{t}{\color{blue}{1}} \]
12. Add Preprocessing

Alternative 20: 19.1% accurate, 2.8× speedup

Math

\[x + \left(t - x\right) \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (- t x)))

C

double code(double x, double y, double z, double t, double a) {
	return x + (t - 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)
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
    code = x + (t - x)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (t - x);
}

Python

def code(x, y, z, t, a):
	return x + (t - x)

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(t - x))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (t - x);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Step-by-step derivation

   1. lower--.f64 19.1

      \[\leadsto x + \left(t - \color{blue}{x}\right) \]

4. Applied rewrites 19.1%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
5. Add Preprocessing

Alternative 21: 2.8% accurate, 3.8× speedup

Math

\[\left(-x\right) + x \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ (- x) x))

C

double code(double x, double y, double z, double t, double a) {
	return -x + 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)
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
    code = -x + x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -x + x;
}

Python

def code(x, y, z, t, a):
	return -x + x

Julia

function code(x, y, z, t, a)
	return Float64(Float64(-x) + x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -x + x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[((-x) + x), $MachinePrecision]

Derivation

1. Initial program 79.9%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Step-by-step derivation

   1. lower--.f64 19.1

      \[\leadsto x + \left(t - \color{blue}{x}\right) \]

4. Applied rewrites 19.1%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto x + -1 \cdot \color{blue}{x} \]
6. Step-by-step derivation

   1. lower-*.f64 2.8

      \[\leadsto x + -1 \cdot x \]

7. Applied rewrites 2.8%

   \[\leadsto x + -1 \cdot \color{blue}{x} \]
8. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + -1 \cdot x} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{-1 \cdot x + x} \]

   3. lower-+.f64 2.8

      \[\leadsto \color{blue}{-1 \cdot x + x} \]

   4. lift-*.f64 N/A

      \[\leadsto -1 \cdot x + x \]

   5. mul-1-neg N/A

      \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

   6. lower-neg.f64 2.8

      \[\leadsto \left(-x\right) + x \]

9. Applied rewrites 2.8%

   \[\leadsto \color{blue}{\left(-x\right) + x} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025172 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))