Data.Colour.RGB:hslsv from colour-2.3.3, B

Percentage Accurate: 99.4% → 99.8%

Time: 4.7s

Alternatives: 19

Speedup: 1.0×

Specification

Math

\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

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 = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

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 = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right) \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma a 120.0 (* (/ -60.0 (- z t)) (- y x))))

C

double code(double x, double y, double z, double t, double a) {
	return fma(a, 120.0, ((-60.0 / (z - t)) * (y - x)));
}

Julia

function code(x, y, z, t, a)
	return fma(a, 120.0, Float64(Float64(-60.0 / Float64(z - t)) * Float64(y - x)))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

   3. lift-/.f64 N/A

      \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   4. mult-flip N/A

      \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

   5. lift-*.f64 N/A

      \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   6. *-commutative N/A

      \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

   7. associate-*l* N/A

      \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

      \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

      \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

       \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

       \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

   12. lift-*.f64 N/A

       \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

   13. lift--.f64 N/A

       \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

   14. sub-negate-rev N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

   15. distribute-rgt-neg-in N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

       \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

   17. sub-negate-rev N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

   18. lift--.f64 N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

   19. associate-*l* N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

   20. *-commutative N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   21. lift-*.f64 N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

3. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]
4. Add Preprocessing

Alternative 2: 90.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (/ (* y -60.0) (- z t)))))
   (if (<= y -1.8e+62)
     t_1
     (if (<= y 1.1e+38) (fma 60.0 (/ x (- z t)) (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((y * -60.0) / (z - t)));
	double tmp;
	if (y <= -1.8e+62) {
		tmp = t_1;
	} else if (y <= 1.1e+38) {
		tmp = fma(60.0, (x / (z - t)), (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(y * -60.0) / Float64(z - t)))
	tmp = 0.0
	if (y <= -1.8e+62)
		tmp = t_1;
	elseif (y <= 1.1e+38)
		tmp = fma(60.0, Float64(x / Float64(z - t)), Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+62], t$95$1, If[LessEqual[y, 1.1e+38], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e62 or 1.10000000000000003e38 < y

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]
   3. Step-by-step derivation

      1. lower-*.f64 74.9%

         \[\leadsto \frac{-60 \cdot \color{blue}{y}}{z - t} + a \cdot 120 \]

   4. Applied rewrites 74.9%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{-60 \cdot y}{z - t}} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{-60 \cdot y}{z - t} \]

      4. lower-fma.f64 74.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60 \cdot \color{blue}{y}}{z - t}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y \cdot \color{blue}{-60}}{z - t}\right) \]

      7. lower-*.f64 74.9%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y \cdot \color{blue}{-60}}{z - t}\right) \]

   6. Applied rewrites 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)} \]

   if -1.8e62 < y < 1.10000000000000003e38

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 82.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.62 \cdot 10^{-126}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{t} \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-93}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.62e-126)
   (fma a 120.0 (* (/ 60.0 t) (- y x)))
   (if (<= t 1.9e-93)
     (fma a 120.0 (* (/ -60.0 z) (- y x)))
     (if (<= t 7.8e-44)
       (* (/ 60.0 (- z t)) (- x y))
       (if (<= t 1.05e+109)
         (fma 60.0 (/ x (- z t)) (* 120.0 a))
         (fma -60.0 (/ (- x y) t) (* 120.0 a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.62e-126) {
		tmp = fma(a, 120.0, ((60.0 / t) * (y - x)));
	} else if (t <= 1.9e-93) {
		tmp = fma(a, 120.0, ((-60.0 / z) * (y - x)));
	} else if (t <= 7.8e-44) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (t <= 1.05e+109) {
		tmp = fma(60.0, (x / (z - t)), (120.0 * a));
	} else {
		tmp = fma(-60.0, ((x - y) / t), (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.62e-126)
		tmp = fma(a, 120.0, Float64(Float64(60.0 / t) * Float64(y - x)));
	elseif (t <= 1.9e-93)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / z) * Float64(y - x)));
	elseif (t <= 7.8e-44)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (t <= 1.05e+109)
		tmp = fma(60.0, Float64(x / Float64(z - t)), Float64(120.0 * a));
	else
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.62e-126], N[(a * 120.0 + N[(N[(60.0 / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-93], N[(a * 120.0 + N[(N[(-60.0 / z), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-44], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+109], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.6199999999999999e-126

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 64.1%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{60}{\color{blue}{t}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 64.1%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot \left(y - x\right)\right) \]

   if -2.6199999999999999e-126 < t < 1.8999999999999999e-93

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 64.2%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   if 1.8999999999999999e-93 < t < 7.8000000000000004e-44

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(x - y\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      12. lower-/.f64 50.1%

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

   6. Applied rewrites 50.1%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

   if 7.8000000000000004e-44 < t < 1.0500000000000001e109

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   if 1.0500000000000001e109 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x - y}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{\color{blue}{t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

      4. lower-*.f64 64.1%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

   4. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 82.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -2.62 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-93}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* 120.0 a))))
   (if (<= t -2.62e-126)
     t_1
     (if (<= t 1.9e-93)
       (fma a 120.0 (* (/ -60.0 z) (- y x)))
       (if (<= t 7.8e-44)
         (* (/ 60.0 (- z t)) (- x y))
         (if (<= t 1.05e+109) (fma 60.0 (/ x (- z t)) (* 120.0 a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (120.0 * a));
	double tmp;
	if (t <= -2.62e-126) {
		tmp = t_1;
	} else if (t <= 1.9e-93) {
		tmp = fma(a, 120.0, ((-60.0 / z) * (y - x)));
	} else if (t <= 7.8e-44) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (t <= 1.05e+109) {
		tmp = fma(60.0, (x / (z - t)), (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(120.0 * a))
	tmp = 0.0
	if (t <= -2.62e-126)
		tmp = t_1;
	elseif (t <= 1.9e-93)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / z) * Float64(y - x)));
	elseif (t <= 7.8e-44)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (t <= 1.05e+109)
		tmp = fma(60.0, Float64(x / Float64(z - t)), Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.62e-126], t$95$1, If[LessEqual[t, 1.9e-93], N[(a * 120.0 + N[(N[(-60.0 / z), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-44], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+109], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6199999999999999e-126 or 1.0500000000000001e109 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x - y}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{\color{blue}{t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

      4. lower-*.f64 64.1%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

   4. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)} \]

   if -2.6199999999999999e-126 < t < 1.8999999999999999e-93

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 64.2%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   if 1.8999999999999999e-93 < t < 7.8000000000000004e-44

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(x - y\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      12. lower-/.f64 50.1%

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

   6. Applied rewrites 50.1%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

   if 7.8000000000000004e-44 < t < 1.0500000000000001e109

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 82.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -2.62 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-93}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* 120.0 a))))
   (if (<= t -2.62e-126)
     t_1
     (if (<= t 1.9e-93)
       (fma 60.0 (/ (- x y) z) (* 120.0 a))
       (if (<= t 7.8e-44)
         (* (/ 60.0 (- z t)) (- x y))
         (if (<= t 1.05e+109) (fma 60.0 (/ x (- z t)) (* 120.0 a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (120.0 * a));
	double tmp;
	if (t <= -2.62e-126) {
		tmp = t_1;
	} else if (t <= 1.9e-93) {
		tmp = fma(60.0, ((x - y) / z), (120.0 * a));
	} else if (t <= 7.8e-44) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (t <= 1.05e+109) {
		tmp = fma(60.0, (x / (z - t)), (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(120.0 * a))
	tmp = 0.0
	if (t <= -2.62e-126)
		tmp = t_1;
	elseif (t <= 1.9e-93)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(120.0 * a));
	elseif (t <= 7.8e-44)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (t <= 1.05e+109)
		tmp = fma(60.0, Float64(x / Float64(z - t)), Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.62e-126], t$95$1, If[LessEqual[t, 1.9e-93], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-44], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+109], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6199999999999999e-126 or 1.0500000000000001e109 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x - y}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{\color{blue}{t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

      4. lower-*.f64 64.1%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

   4. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)} \]

   if -2.6199999999999999e-126 < t < 1.8999999999999999e-93

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x - y}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{\color{blue}{z}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

      4. lower-*.f64 64.2%

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

   4. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]

   if 1.8999999999999999e-93 < t < 7.8000000000000004e-44

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(x - y\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      12. lower-/.f64 50.1%

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

   6. Applied rewrites 50.1%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

   if 7.8000000000000004e-44 < t < 1.0500000000000001e109

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 79.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-10}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e-10)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= t_1 5e-22)
       (fma 60.0 (/ x (- z t)) (* 120.0 a))
       (* (/ 60.0 (- z t)) (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e-10) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= 5e-22) {
		tmp = fma(60.0, (x / (z - t)), (120.0 * a));
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e-10)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t_1 <= 5e-22)
		tmp = fma(60.0, Float64(x / Float64(z - t)), Float64(120.0 * a));
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-10], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-22], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000031e-10

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   if -5.00000000000000031e-10 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999954e-22

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   if 4.99999999999999954e-22 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(x - y\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      12. lower-/.f64 50.1%

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

   6. Applied rewrites 50.1%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -2.62 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-233}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{-32}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* 120.0 a))))
   (if (<= t -2.62e-126)
     t_1
     (if (<= t -4.6e-233)
       (fma 60.0 (/ x z) (* 120.0 a))
       (if (<= t 1.04e-32)
         (* (/ 60.0 (- z t)) (- x y))
         (if (<= t 2.9e+56) (fma a 120.0 (* (/ -60.0 z) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (120.0 * a));
	double tmp;
	if (t <= -2.62e-126) {
		tmp = t_1;
	} else if (t <= -4.6e-233) {
		tmp = fma(60.0, (x / z), (120.0 * a));
	} else if (t <= 1.04e-32) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (t <= 2.9e+56) {
		tmp = fma(a, 120.0, ((-60.0 / z) * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(120.0 * a))
	tmp = 0.0
	if (t <= -2.62e-126)
		tmp = t_1;
	elseif (t <= -4.6e-233)
		tmp = fma(60.0, Float64(x / z), Float64(120.0 * a));
	elseif (t <= 1.04e-32)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (t <= 2.9e+56)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / z) * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.62e-126], t$95$1, If[LessEqual[t, -4.6e-233], N[(60.0 * N[(x / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.04e-32], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+56], N[(a * 120.0 + N[(N[(-60.0 / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6199999999999999e-126 or 2.90000000000000007e56 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x - y}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{\color{blue}{t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

      4. lower-*.f64 64.1%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

   4. Applied rewrites 64.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)} \]

   if -2.6199999999999999e-126 < t < -4.6000000000000004e-233

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 55.9%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right) \]

   7. Applied rewrites 55.9%

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]

   if -4.6000000000000004e-233 < t < 1.03999999999999998e-32

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(x - y\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      12. lower-/.f64 50.1%

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

   6. Applied rewrites 50.1%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

   if 1.03999999999999998e-32 < t < 2.90000000000000007e56

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 64.2%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{60}{t} \cdot y\right)\\ \mathbf{if}\;a \leq -9.6 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-70}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* (/ 60.0 t) y))))
   (if (<= a -9.6e+78)
     t_1
     (if (<= a 1.45e-70)
       (* 60.0 (/ (- x y) (- z t)))
       (if (<= a 2.5e+72) t_1 (fma a 120.0 (* (/ -60.0 z) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((60.0 / t) * y));
	double tmp;
	if (a <= -9.6e+78) {
		tmp = t_1;
	} else if (a <= 1.45e-70) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (a <= 2.5e+72) {
		tmp = t_1;
	} else {
		tmp = fma(a, 120.0, ((-60.0 / z) * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(60.0 / t) * y))
	tmp = 0.0
	if (a <= -9.6e+78)
		tmp = t_1;
	elseif (a <= 1.45e-70)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (a <= 2.5e+72)
		tmp = t_1;
	else
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / z) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(60.0 / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.6e+78], t$95$1, If[LessEqual[a, 1.45e-70], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+72], t$95$1, N[(a * 120.0 + N[(N[(-60.0 / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5999999999999994e78 or 1.44999999999999986e-70 < a < 2.49999999999999996e72

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 64.2%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]

   10. Taylor expanded in z around 0

       \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot y\right) \]
   11. Step-by-step derivation

       1. lower-/.f64 55.3%

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{60}{\color{blue}{t}} \cdot y\right) \]

   12. Applied rewrites 55.3%

       \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot y\right) \]

   if -9.5999999999999994e78 < a < 1.44999999999999986e-70

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   if 2.49999999999999996e72 < a

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 64.2%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 66.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-147}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{t} \cdot y\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-196}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e-147)
   (fma a 120.0 (* (/ 60.0 t) y))
   (if (<= t 3.3e-196)
     (* 60.0 (/ (- x y) z))
     (if (<= t 2.9e+56)
       (fma a 120.0 (* (/ -60.0 z) y))
       (fma -60.0 (/ x t) (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e-147) {
		tmp = fma(a, 120.0, ((60.0 / t) * y));
	} else if (t <= 3.3e-196) {
		tmp = 60.0 * ((x - y) / z);
	} else if (t <= 2.9e+56) {
		tmp = fma(a, 120.0, ((-60.0 / z) * y));
	} else {
		tmp = fma(-60.0, (x / t), (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e-147)
		tmp = fma(a, 120.0, Float64(Float64(60.0 / t) * y));
	elseif (t <= 3.3e-196)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (t <= 2.9e+56)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / z) * y));
	else
		tmp = fma(-60.0, Float64(x / t), Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e-147], N[(a * 120.0 + N[(N[(60.0 / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-196], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+56], N[(a * 120.0 + N[(N[(-60.0 / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.49999999999999973e-147

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 64.2%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]

   10. Taylor expanded in z around 0

       \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot y\right) \]
   11. Step-by-step derivation

       1. lower-/.f64 55.3%

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{60}{\color{blue}{t}} \cdot y\right) \]

   12. Applied rewrites 55.3%

       \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot y\right) \]

   if -4.49999999999999973e-147 < t < 3.29999999999999999e-196

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around inf

      \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{z} \]

      2. lower--.f64 28.1%

         \[\leadsto 60 \cdot \frac{x - y}{z} \]

   7. Applied rewrites 28.1%

      \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z}} \]

   if 3.29999999999999999e-196 < t < 2.90000000000000007e56

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 64.2%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]

   if 2.90000000000000007e56 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \frac{x}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{\color{blue}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

      3. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

   7. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x}{t}}, 120 \cdot a\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -2.62 \cdot 10^{-126}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-44}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ x z) (* 120.0 a))))
   (if (<= t -2.62e-126)
     (fma a 120.0 (* (/ x t) -60.0))
     (if (<= t 1.9e-93)
       t_1
       (if (<= t 7.8e-44)
         (* -60.0 (/ y (- z t)))
         (if (<= t 2.9e+56) t_1 (fma -60.0 (/ x t) (* 120.0 a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(60.0, (x / z), (120.0 * a));
	double tmp;
	if (t <= -2.62e-126) {
		tmp = fma(a, 120.0, ((x / t) * -60.0));
	} else if (t <= 1.9e-93) {
		tmp = t_1;
	} else if (t <= 7.8e-44) {
		tmp = -60.0 * (y / (z - t));
	} else if (t <= 2.9e+56) {
		tmp = t_1;
	} else {
		tmp = fma(-60.0, (x / t), (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(x / z), Float64(120.0 * a))
	tmp = 0.0
	if (t <= -2.62e-126)
		tmp = fma(a, 120.0, Float64(Float64(x / t) * -60.0));
	elseif (t <= 1.9e-93)
		tmp = t_1;
	elseif (t <= 7.8e-44)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t <= 2.9e+56)
		tmp = t_1;
	else
		tmp = fma(-60.0, Float64(x / t), Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.62e-126], N[(a * 120.0 + N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-93], t$95$1, If[LessEqual[t, 7.8e-44], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+56], t$95$1, N[(-60.0 * N[(x / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6199999999999999e-126

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \frac{x}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{\color{blue}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

      3. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

   7. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x}{t}}, 120 \cdot a\right) \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} + 120 \cdot \color{blue}{a} \]

      2. lift-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} + 120 \cdot a \]

      3. *-commutative N/A

         \[\leadsto -60 \cdot \frac{x}{t} + a \cdot 120 \]

      4. +-commutative N/A

         \[\leadsto a \cdot 120 + -60 \cdot \color{blue}{\frac{x}{t}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, -60 \cdot \frac{x}{t}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right) \]

      7. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right) \]

   9. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right) \]

   if -2.6199999999999999e-126 < t < 1.8999999999999999e-93 or 7.8000000000000004e-44 < t < 2.90000000000000007e56

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 55.9%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right) \]

   7. Applied rewrites 55.9%

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]

   if 1.8999999999999999e-93 < t < 7.8000000000000004e-44

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Taylor expanded in x around inf

      \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} \]

      2. lower-/.f64 16.3%

         \[\leadsto -60 \cdot \frac{x}{t} \]

   10. Applied rewrites 16.3%

       \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]

   11. Taylor expanded in x around 0

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto -60 \cdot \frac{y}{\color{blue}{z - t}} \]

       2. lower-/.f64 N/A

          \[\leadsto -60 \cdot \frac{y}{z - \color{blue}{t}} \]

       3. lower--.f64 26.0%

          \[\leadsto -60 \cdot \frac{y}{z - t} \]

   13. Applied rewrites 26.0%

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]

   if 2.90000000000000007e56 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \frac{x}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{\color{blue}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

      3. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

   7. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x}{t}}, 120 \cdot a\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 63.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.62 \cdot 10^{-126}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.62e-126)
   (fma a 120.0 (* (/ x t) -60.0))
   (if (<= t 2.9e+56)
     (fma a 120.0 (* (/ -60.0 z) y))
     (fma -60.0 (/ x t) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.62e-126) {
		tmp = fma(a, 120.0, ((x / t) * -60.0));
	} else if (t <= 2.9e+56) {
		tmp = fma(a, 120.0, ((-60.0 / z) * y));
	} else {
		tmp = fma(-60.0, (x / t), (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.62e-126)
		tmp = fma(a, 120.0, Float64(Float64(x / t) * -60.0));
	elseif (t <= 2.9e+56)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / z) * y));
	else
		tmp = fma(-60.0, Float64(x / t), Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.62e-126], N[(a * 120.0 + N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+56], N[(a * 120.0 + N[(N[(-60.0 / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6199999999999999e-126

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \frac{x}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{\color{blue}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

      3. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

   7. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x}{t}}, 120 \cdot a\right) \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} + 120 \cdot \color{blue}{a} \]

      2. lift-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} + 120 \cdot a \]

      3. *-commutative N/A

         \[\leadsto -60 \cdot \frac{x}{t} + a \cdot 120 \]

      4. +-commutative N/A

         \[\leadsto a \cdot 120 + -60 \cdot \color{blue}{\frac{x}{t}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, -60 \cdot \frac{x}{t}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right) \]

      7. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right) \]

   9. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right) \]

   if -2.6199999999999999e-126 < t < 2.90000000000000007e56

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

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

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 64.2%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]

   if 2.90000000000000007e56 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \frac{x}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{\color{blue}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

      3. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

   7. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x}{t}}, 120 \cdot a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-139}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{elif}\;t \leq 170000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e-139)
   (fma a 120.0 (* (/ x t) -60.0))
   (if (<= t 170000000.0)
     (* 60.0 (/ (- x y) z))
     (fma -60.0 (/ x t) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e-139) {
		tmp = fma(a, 120.0, ((x / t) * -60.0));
	} else if (t <= 170000000.0) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = fma(-60.0, (x / t), (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e-139)
		tmp = fma(a, 120.0, Float64(Float64(x / t) * -60.0));
	elseif (t <= 170000000.0)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = fma(-60.0, Float64(x / t), Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e-139], N[(a * 120.0 + N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 170000000.0], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.00000000000000002e-139

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \frac{x}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{\color{blue}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

      3. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

   7. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x}{t}}, 120 \cdot a\right) \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} + 120 \cdot \color{blue}{a} \]

      2. lift-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} + 120 \cdot a \]

      3. *-commutative N/A

         \[\leadsto -60 \cdot \frac{x}{t} + a \cdot 120 \]

      4. +-commutative N/A

         \[\leadsto a \cdot 120 + -60 \cdot \color{blue}{\frac{x}{t}} \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, -60 \cdot \frac{x}{t}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right) \]

      7. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right) \]

   9. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right) \]

   if -7.00000000000000002e-139 < t < 1.7e8

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around inf

      \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{z} \]

      2. lower--.f64 28.1%

         \[\leadsto 60 \cdot \frac{x - y}{z} \]

   7. Applied rewrites 28.1%

      \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z}} \]

   if 1.7e8 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \frac{x}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{\color{blue}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

      3. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

   7. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x}{t}}, 120 \cdot a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 170000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ x t) (* 120.0 a))))
   (if (<= t -7e-139) t_1 (if (<= t 170000000.0) (* 60.0 (/ (- x y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, (x / t), (120.0 * a));
	double tmp;
	if (t <= -7e-139) {
		tmp = t_1;
	} else if (t <= 170000000.0) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(x / t), Float64(120.0 * a))
	tmp = 0.0
	if (t <= -7e-139)
		tmp = t_1;
	elseif (t <= 170000000.0)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-139], t$95$1, If[LessEqual[t, 170000000.0], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000002e-139 or 1.7e8 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x}{z - t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z - t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - \color{blue}{t}}, 120 \cdot a\right) \]

      4. lower-*.f64 76.0%

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right) \]

   4. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x}{z - t}, 120 \cdot a\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \frac{x}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{\color{blue}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

      3. lower-*.f64 55.4%

         \[\leadsto \mathsf{fma}\left(-60, \frac{x}{t}, 120 \cdot a\right) \]

   7. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x}{t}}, 120 \cdot a\right) \]

   if -7.00000000000000002e-139 < t < 1.7e8

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around inf

      \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{z} \]

      2. lower--.f64 28.1%

         \[\leadsto 60 \cdot \frac{x - y}{z} \]

   7. Applied rewrites 28.1%

      \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 55.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-10}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-22}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot \left(x - y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e-10)
     (* -60.0 (/ y (- z t)))
     (if (<= t_1 5e-22) (* 120.0 a) (* (/ -60.0 t) (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e-10) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= 5e-22) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * (x - y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d-10)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_1 <= 5d-22) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) / t) * (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e-10) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= 5e-22) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e-10:
		tmp = -60.0 * (y / (z - t))
	elif t_1 <= 5e-22:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 / t) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e-10)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_1 <= 5e-22)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 / t) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e-10)
		tmp = -60.0 * (y / (z - t));
	elseif (t_1 <= 5e-22)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 / t) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-10], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-22], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000031e-10

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Taylor expanded in x around inf

      \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} \]

      2. lower-/.f64 16.3%

         \[\leadsto -60 \cdot \frac{x}{t} \]

   10. Applied rewrites 16.3%

       \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]

   11. Taylor expanded in x around 0

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto -60 \cdot \frac{y}{\color{blue}{z - t}} \]

       2. lower-/.f64 N/A

          \[\leadsto -60 \cdot \frac{y}{z - \color{blue}{t}} \]

       3. lower--.f64 26.0%

          \[\leadsto -60 \cdot \frac{y}{z - t} \]

   13. Applied rewrites 26.0%

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]

   if -5.00000000000000031e-10 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999954e-22

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.4%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 4.99999999999999954e-22 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      3. lift--.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      5. mult-flip N/A

         \[\leadsto \left(\left(x - y\right) \cdot \frac{1}{t}\right) \cdot -60 \]

      6. associate-*l* N/A

         \[\leadsto \left(x - y\right) \cdot \left(\frac{1}{t} \cdot \color{blue}{-60}\right) \]

      7. *-commutative N/A

         \[\leadsto \left(\frac{1}{t} \cdot -60\right) \cdot \left(x - \color{blue}{y}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{t} \cdot -60\right) \cdot \left(x - \color{blue}{y}\right) \]

      9. metadata-eval N/A

         \[\leadsto \left(\frac{\mathsf{neg}\left(-1\right)}{t} \cdot -60\right) \cdot \left(x - y\right) \]

      10. associate-*l/ N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(-1\right)\right) \cdot -60}{t} \cdot \left(x - y\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{1 \cdot -60}{t} \cdot \left(x - y\right) \]

      12. metadata-eval N/A

          \[\leadsto \frac{-60}{t} \cdot \left(x - y\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \frac{-60}{t} \cdot \left(x - y\right) \]

      14. lift--.f64 28.2%

          \[\leadsto \frac{-60}{t} \cdot \left(x - y\right) \]

   9. Applied rewrites 28.2%

      \[\leadsto \frac{-60}{t} \cdot \left(x - \color{blue}{y}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 55.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-10}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-22}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e-10)
     (* -60.0 (/ y (- z t)))
     (if (<= t_1 5e-22) (* 120.0 a) (* -60.0 (/ (- x y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e-10) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= 5e-22) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d-10)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_1 <= 5d-22) then
        tmp = 120.0d0 * a
    else
        tmp = (-60.0d0) * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e-10) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= 5e-22) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e-10:
		tmp = -60.0 * (y / (z - t))
	elif t_1 <= 5e-22:
		tmp = 120.0 * a
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e-10)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_1 <= 5e-22)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e-10)
		tmp = -60.0 * (y / (z - t));
	elseif (t_1 <= 5e-22)
		tmp = 120.0 * a;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-10], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-22], N[(120.0 * a), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000031e-10

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Taylor expanded in x around inf

      \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} \]

      2. lower-/.f64 16.3%

         \[\leadsto -60 \cdot \frac{x}{t} \]

   10. Applied rewrites 16.3%

       \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]

   11. Taylor expanded in x around 0

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto -60 \cdot \frac{y}{\color{blue}{z - t}} \]

       2. lower-/.f64 N/A

          \[\leadsto -60 \cdot \frac{y}{z - \color{blue}{t}} \]

       3. lower--.f64 26.0%

          \[\leadsto -60 \cdot \frac{y}{z - t} \]

   13. Applied rewrites 26.0%

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]

   if -5.00000000000000031e-10 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999954e-22

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.4%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 4.99999999999999954e-22 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 55.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-22}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e-10) t_1 (if (<= t_2 5e-22) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e-10) {
		tmp = t_1;
	} else if (t_2 <= 5e-22) {
		tmp = 120.0 * 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) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d-10)) then
        tmp = t_1
    else if (t_2 <= 5d-22) then
        tmp = 120.0d0 * 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 = -60.0 * (y / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e-10) {
		tmp = t_1;
	} else if (t_2 <= 5e-22) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e-10:
		tmp = t_1
	elif t_2 <= 5e-22:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e-10)
		tmp = t_1;
	elseif (t_2 <= 5e-22)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e-10)
		tmp = t_1;
	elseif (t_2 <= 5e-22)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-10], t$95$1, If[LessEqual[t$95$2, 5e-22], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000031e-10 or 4.99999999999999954e-22 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Taylor expanded in x around inf

      \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} \]

      2. lower-/.f64 16.3%

         \[\leadsto -60 \cdot \frac{x}{t} \]

   10. Applied rewrites 16.3%

       \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]

   11. Taylor expanded in x around 0

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto -60 \cdot \frac{y}{\color{blue}{z - t}} \]

       2. lower-/.f64 N/A

          \[\leadsto -60 \cdot \frac{y}{z - \color{blue}{t}} \]

       3. lower--.f64 26.0%

          \[\leadsto -60 \cdot \frac{y}{z - t} \]

   13. Applied rewrites 26.0%

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]

   if -5.00000000000000031e-10 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999954e-22

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.4%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 54.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+138}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ y t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+178) t_1 (if (<= t_2 1e+138) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (y / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+178) {
		tmp = t_1;
	} else if (t_2 <= 1e+138) {
		tmp = 120.0 * 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) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * (y / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+178)) then
        tmp = t_1
    else if (t_2 <= 1d+138) then
        tmp = 120.0d0 * 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 = 60.0 * (y / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+178) {
		tmp = t_1;
	} else if (t_2 <= 1e+138) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (y / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+178:
		tmp = t_1
	elif t_2 <= 1e+138:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(y / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+178)
		tmp = t_1;
	elseif (t_2 <= 1e+138)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (y / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+178)
		tmp = t_1;
	elseif (t_2 <= 1e+138)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+178], t$95$1, If[LessEqual[t$95$2, 1e+138], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.0000000000000001e178 or 1e138 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Taylor expanded in x around 0

      \[\leadsto 60 \cdot \frac{y}{\color{blue}{t}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \frac{y}{t} \]

      2. lower-/.f64 15.6%

         \[\leadsto 60 \cdot \frac{y}{t} \]

   10. Applied rewrites 15.6%

       \[\leadsto 60 \cdot \frac{y}{\color{blue}{t}} \]

   if -1.0000000000000001e178 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e138

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.4%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 51.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 9.6 \cdot 10^{+103}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 9.6e+103) (* 120.0 a) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 9.6e+103) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
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) :: tmp
    if (x <= 9.6d+103) then
        tmp = 120.0d0 * a
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 9.6e+103) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 9.6e+103:
		tmp = 120.0 * a
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 9.6e+103)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 9.6e+103)
		tmp = 120.0 * a;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 9.6e+103], N[(120.0 * a), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.5999999999999994e103

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 51.4%

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 9.5999999999999994e103 < x

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 50.1%

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 50.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 28.2%

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 28.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Taylor expanded in x around inf

      \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{t} \]

      2. lower-/.f64 16.3%

         \[\leadsto -60 \cdot \frac{x}{t} \]

   10. Applied rewrites 16.3%

       \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 51.2% accurate, 4.6× speedup

Math

\[120 \cdot a \]

FPCore

(FPCore (x y z t a) :precision binary64 (* 120.0 a))

C

double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

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 = 120.0d0 * a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

Python

def code(x, y, z, t, a):
	return 120.0 * a

Julia

function code(x, y, z, t, a)
	return Float64(120.0 * a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 120.0 * a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(120.0 * a), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
3. Step-by-step derivation

   1. lower-*.f64 51.4%

      \[\leadsto 120 \cdot \color{blue}{a} \]

4. Applied rewrites 51.4%

   \[\leadsto \color{blue}{120 \cdot a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025184 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64
  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))