Main:z from

Average Error: 5.1 → 3.9

Time: 1.2min

Precision: binary64

Cost: 65988

Math

\[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

↓

\[\begin{array}{l} t_1 := \sqrt{z + 1}\\ t_2 := t_1 + \sqrt{z}\\ \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \begin{array}{l} \mathbf{if}\;t_2 \ne 0:\\ \;\;\;\;\frac{1}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1 - \sqrt{z}\\ \end{array}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ z 1.0))) (t_2 (+ t_1 (sqrt z))))
   (+
    (+
     (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y)))
     (if (!= t_2 0.0) (/ 1.0 t_2) (- t_1 (sqrt z))))
    (- (sqrt (+ t 1.0)) (sqrt t)))))

C

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

↓

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z + 1.0));
	double t_2 = t_1 + sqrt(z);
	double tmp;
	if (t_2 != 0.0) {
		tmp = 1.0 / t_2;
	} else {
		tmp = t_1 - sqrt(z);
	}
	return (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + tmp) + (sqrt((t + 1.0)) - sqrt(t));
}

Fortran

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

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = sqrt((z + 1.0d0))
    t_2 = t_1 + sqrt(z)
    if (t_2 /= 0.0d0) then
        tmp = 1.0d0 / t_2
    else
        tmp = t_1 - sqrt(z)
    end if
    code = (((sqrt((x + 1.0d0)) - sqrt(x)) + (sqrt((y + 1.0d0)) - sqrt(y))) + tmp) + (sqrt((t + 1.0d0)) - sqrt(t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((Math.sqrt((x + 1.0)) - Math.sqrt(x)) + (Math.sqrt((y + 1.0)) - Math.sqrt(y))) + (Math.sqrt((z + 1.0)) - Math.sqrt(z))) + (Math.sqrt((t + 1.0)) - Math.sqrt(t));
}

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z + 1.0));
	double t_2 = t_1 + Math.sqrt(z);
	double tmp;
	if (t_2 != 0.0) {
		tmp = 1.0 / t_2;
	} else {
		tmp = t_1 - Math.sqrt(z);
	}
	return (((Math.sqrt((x + 1.0)) - Math.sqrt(x)) + (Math.sqrt((y + 1.0)) - Math.sqrt(y))) + tmp) + (Math.sqrt((t + 1.0)) - Math.sqrt(t));
}

Python

def code(x, y, z, t):
	return (((math.sqrt((x + 1.0)) - math.sqrt(x)) + (math.sqrt((y + 1.0)) - math.sqrt(y))) + (math.sqrt((z + 1.0)) - math.sqrt(z))) + (math.sqrt((t + 1.0)) - math.sqrt(t))

↓

def code(x, y, z, t):
	t_1 = math.sqrt((z + 1.0))
	t_2 = t_1 + math.sqrt(z)
	tmp = 0
	if t_2 != 0.0:
		tmp = 1.0 / t_2
	else:
		tmp = t_1 - math.sqrt(z)
	return (((math.sqrt((x + 1.0)) - math.sqrt(x)) + (math.sqrt((y + 1.0)) - math.sqrt(y))) + tmp) + (math.sqrt((t + 1.0)) - math.sqrt(t))

Julia

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

↓

function code(x, y, z, t)
	t_1 = sqrt(Float64(z + 1.0))
	t_2 = Float64(t_1 + sqrt(z))
	tmp = 0.0
	if (t_2 != 0.0)
		tmp = Float64(1.0 / t_2);
	else
		tmp = Float64(t_1 - sqrt(z));
	end
	return Float64(Float64(Float64(Float64(sqrt(Float64(x + 1.0)) - sqrt(x)) + Float64(sqrt(Float64(y + 1.0)) - sqrt(y))) + tmp) + Float64(sqrt(Float64(t + 1.0)) - sqrt(t)))
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z + 1.0));
	t_2 = t_1 + sqrt(z);
	tmp = 0.0;
	if (t_2 ~= 0.0)
		tmp = 1.0 / t_2;
	else
		tmp = t_1 - sqrt(z);
	end
	tmp_2 = (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + tmp) + (sqrt((t + 1.0)) - sqrt(t));
end

Wolfram

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

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(y + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + If[Unequal[t$95$2, 0.0], N[(1.0 / t$95$2), $MachinePrecision], N[(t$95$1 - N[Sqrt[z], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision] + N[(N[Sqrt[N[(t + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	5.1
Target	1.5
Herbie	3.9

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

Derivation

1. Initial program 5.1

   \[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

2. Applied egg-rr 5.0

   \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\sqrt{z + 1} + \sqrt{z} \ne 0:\\ \;\;\;\;\frac{{\left(\sqrt{z + 1}\right)}^{2} - {\left(\sqrt{z}\right)}^{2}}{\sqrt{z + 1} + \sqrt{z}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z + 1} - \sqrt{z}\\ } \end{array}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

3. Taylor expanded in z around 0 3.9

   \[\leadsto \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \begin{array}{l} \mathbf{if}\;\sqrt{z + 1} + \sqrt{z} \ne 0:\\ \;\;\;\;\frac{\color{blue}{1}}{\sqrt{z + 1} + \sqrt{z}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z + 1} - \sqrt{z}\\ \end{array}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

Alternatives

Alternative 1
Error	5.1
Cost	65536

\[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \sqrt[3]{{\left(\sqrt{z + 1} - \sqrt{z}\right)}^{3}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

Alternative 2
Error	16.7
Cost	52944

\[\begin{array}{l} t_1 := \sqrt{t + 1}\\ t_2 := t_1 + \sqrt{t}\\ t_3 := t_1 - \sqrt{t}\\ t_4 := 1 + t_3\\ t_5 := \sqrt{x + 1} - \sqrt{x}\\ t_6 := \left(\left(t_5 + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + 1\right) + t_3\\ \mathbf{if}\;y \leq 2.3 \cdot 10^{-21}:\\ \;\;\;\;\left(\left(t_5 + 1\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + t_3\\ \mathbf{elif}\;y \leq 165000:\\ \;\;\;\;\left(\left(\sqrt{t - -1} - \sqrt{t}\right) - \left(\sqrt{z} - \left(\sqrt{z - -1} + 1\right)\right)\right) + \left(\sqrt{y - -1} - \sqrt{y}\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+119}:\\ \;\;\;\;1 + \begin{array}{l} \mathbf{if}\;t_2 \ne 0:\\ \;\;\;\;\frac{{t_1}^{2} - {\left(\sqrt{t}\right)}^{2}}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array}\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+162}:\\ \;\;\;\;\left(\left(1 - \sqrt{z}\right) + \sqrt{1 + z}\right) + t_3\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+195}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+254}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+282}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 3
Error	5.1
Cost	52672

\[\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \]

Alternative 4
Error	16.7
Cost	40540

\[\begin{array}{l} t_1 := \sqrt{t + 1} - \sqrt{t}\\ t_2 := \sqrt{x + 1} - \sqrt{x}\\ t_3 := \left(\left(t_2 + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + 1\right) + t_1\\ t_4 := 1 + t_1\\ \mathbf{if}\;y \leq 2.3 \cdot 10^{-21}:\\ \;\;\;\;\left(\left(t_2 + 1\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + t_1\\ \mathbf{elif}\;y \leq 165000:\\ \;\;\;\;\left(\left(\sqrt{t - -1} - \sqrt{t}\right) - \left(\sqrt{z} - \left(\sqrt{z - -1} + 1\right)\right)\right) + \left(\sqrt{y - -1} - \sqrt{y}\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+119}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+162}:\\ \;\;\;\;\left(\left(1 - \sqrt{z}\right) + \sqrt{1 + z}\right) + t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+190}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.26 \cdot 10^{+254}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+282}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	16.0
Cost	40012

\[\begin{array}{l} t_1 := \sqrt{t + 1}\\ t_2 := t_1 - \sqrt{t}\\ t_3 := \sqrt{x + 1} - \sqrt{x}\\ t_4 := \left(\left(t_3 + 1\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + t_2\\ t_5 := -\sqrt{t}\\ \mathbf{if}\;z \leq 7.5 \cdot 10^{-18}:\\ \;\;\;\;\left(\left(t_3 + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + 1\right) + t_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+39}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+142}:\\ \;\;\;\;1 + \begin{array}{l} \mathbf{if}\;t_5 \ne 0:\\ \;\;\;\;t_5 \cdot \left(1 + \frac{t_1}{t_5}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 6
Error	16.1
Cost	39880

\[\begin{array}{l} t_1 := \sqrt{z + 1} - \sqrt{z}\\ t_2 := \sqrt{t + 1}\\ t_3 := t_2 - \sqrt{t}\\ t_4 := -\sqrt{t}\\ \mathbf{if}\;x \leq 7.4 \cdot 10^{-10}:\\ \;\;\;\;\left(\left(1 + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + t_1\right) + t_3\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+136}:\\ \;\;\;\;\left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + 1\right) + t_1\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;1 + \begin{array}{l} \mathbf{if}\;t_4 \ne 0:\\ \;\;\;\;t_4 \cdot \left(1 + \frac{t_2}{t_4}\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array}\\ \end{array} \]

Alternative 7
Error	17.5
Cost	39748

\[\begin{array}{l} t_1 := \sqrt{t + 1}\\ t_2 := t_1 - \sqrt{t}\\ t_3 := -\sqrt{t}\\ \mathbf{if}\;x \leq 1.35:\\ \;\;\;\;\left(\left(1 + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + t_2\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+179}:\\ \;\;\;\;1 + {\left(\sqrt[3]{t_2}\right)}^{3}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+217}:\\ \;\;\;\;\left(\left(1 - \sqrt{z}\right) + \sqrt{1 + z}\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;1 + \begin{array}{l} \mathbf{if}\;t_3 \ne 0:\\ \;\;\;\;t_3 \cdot \left(1 + \frac{t_1}{t_3}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array}\\ \end{array} \]

Alternative 8
Error	31.5
Cost	27092

\[\begin{array}{l} t_1 := \sqrt{t + 1} - \sqrt{t}\\ t_2 := \left(\sqrt{1 + y} + \left(1 - \sqrt{y}\right)\right) + t_1\\ t_3 := 1 + t_1\\ \mathbf{if}\;z \leq 5.4 \cdot 10^{-15}:\\ \;\;\;\;2 + t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+34}:\\ \;\;\;\;\left(\sqrt{1 + z} + \left(2 - \sqrt{z}\right)\right) + t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+214}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	29.8
Cost	27092

\[\begin{array}{l} t_1 := \sqrt{t + 1} - \sqrt{t}\\ t_2 := 1 + t_1\\ t_3 := \left(\left(1 - \sqrt{z}\right) + \sqrt{1 + z}\right) + t_1\\ \mathbf{if}\;y \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\left(\sqrt{1 + y} + \left(1 - \sqrt{y}\right)\right) + t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+162}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+241}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	29.9
Cost	26564

\[\begin{array}{l} t_1 := \sqrt{t + 1} - \sqrt{t}\\ t_2 := 1 + t_1\\ \mathbf{if}\;y \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\left(\sqrt{1 + y} + \left(1 - \sqrt{y}\right)\right) + t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+162}:\\ \;\;\;\;2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	30.3
Cost	20292

\[\begin{array}{l} t_1 := \sqrt{t + 1} - \sqrt{t}\\ t_2 := 1 + t_1\\ \mathbf{if}\;y \leq 2.3:\\ \;\;\;\;\left(\left(y \cdot 0.5 - -1\right) + \left(1 - \sqrt{y}\right)\right) + t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+162}:\\ \;\;\;\;2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	31.1
Cost	13644

\[\begin{array}{l} t_1 := \sqrt{t + 1} - \sqrt{t}\\ t_2 := 1 + t_1\\ t_3 := 2 + t_1\\ \mathbf{if}\;y \leq 2.5 \cdot 10^{-32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+162}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	35.3
Cost	13512

\[\begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{-18}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+108}:\\ \;\;\;\;1 + \left(\sqrt{t + 1} - \sqrt{t}\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+257}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14
Error	35.9
Cost	592

\[\begin{array}{l} \mathbf{if}\;z \leq 15000000000000:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+123}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+168}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 15
Error	41.9
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z t)
  :name "Main:z from "
  :precision binary64

  :herbie-target
  (+ (+ (+ (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))) (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (- (sqrt (+ t 1.0)) (sqrt t)))

  (+ (+ (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y))) (- (sqrt (+ z 1.0)) (sqrt z))) (- (sqrt (+ t 1.0)) (sqrt t))))