Average Error: 27.7 → 2.4
Time: 13.1s
Precision: binary64
Cost: 20160
\[\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)}\]
↓
\[\frac{\frac{\frac{\cos \left(x \cdot 2\right)}{c}}{\left|x \cdot s\right|}}{c \cdot \left|x \cdot s\right|}\]
\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)}
↓
\frac{\frac{\frac{\cos \left(x \cdot 2\right)}{c}}{\left|x \cdot s\right|}}{c \cdot \left|x \cdot s\right|}
(FPCore (x c s)
 :precision binary64
 (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))
↓
(FPCore (x c s)
 :precision binary64
 (/ (/ (/ (cos (* x 2.0)) c) (fabs (* x s))) (* c (fabs (* x s)))))
double code(double x, double c, double s) {
	return cos(2.0 * x) / (pow(c, 2.0) * ((x * pow(s, 2.0)) * x));
}
↓
double code(double x, double c, double s) {
	return ((cos(x * 2.0) / c) / fabs(x * s)) / (c * fabs(x * s));
}

Error

Bits error versus x

Bits error versus c

Bits error versus s

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error19.9
Cost79232
\[\sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(c \cdot c\right)}} \cdot \left(\sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(c \cdot c\right)}} \cdot \sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(c \cdot c\right)}}\right)\]
Alternative 2
Error3.1
Cost78848
\[\sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}} \cdot \left(\sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}} \cdot \sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}}\right)\]
Alternative 3
Error2.8
Cost66240
\[\frac{\sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}} \cdot \left(\sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}} \cdot \sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}}\right)}{c \cdot \left|x \cdot s\right|}\]
Alternative 4
Error20.0
Cost65920
\[\frac{\cos \left(x \cdot 2\right)}{\sqrt[3]{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(c \cdot c\right)} \cdot \left(\sqrt[3]{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(c \cdot c\right)} \cdot \sqrt[3]{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(c \cdot c\right)}\right)}\]
Alternative 5
Error3.1
Cost65536
\[\frac{\frac{\cos \left(x \cdot 2\right)}{\sqrt[3]{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}} \cdot \sqrt[3]{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}}}{\sqrt[3]{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}}\]
Alternative 6
Error2.8
Cost52928
\[\frac{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}}{\sqrt[3]{c \cdot \left|x \cdot s\right|} \cdot \left(\sqrt[3]{c \cdot \left|x \cdot s\right|} \cdot \sqrt[3]{c \cdot \left|x \cdot s\right|}\right)}\]
Alternative 7
Error23.6
Cost52800
\[\sqrt{\frac{\cos \left(x \cdot 2\right)}{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(c \cdot c\right)}} \cdot \sqrt{\frac{\cos \left(x \cdot 2\right)}{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(c \cdot c\right)}}\]
Alternative 8
Error2.6
Cost52672
\[\frac{\sqrt[3]{\cos \left(x \cdot 2\right)} \cdot \sqrt[3]{\cos \left(x \cdot 2\right)}}{c \cdot \left|x \cdot s\right|} \cdot \frac{\sqrt[3]{\cos \left(x \cdot 2\right)}}{c \cdot \left|x \cdot s\right|}\]
Alternative 9
Error10.3
Cost52544
\[\sqrt{\frac{\cos \left(x \cdot 2\right)}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}} \cdot \sqrt{\frac{\cos \left(x \cdot 2\right)}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}}\]
Alternative 10
Error20.1
Cost52480
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left({\left(\sqrt[3]{\left|x \cdot s\right|}\right)}^{4} \cdot \left(\sqrt[3]{\left|x \cdot s\right|} \cdot \sqrt[3]{\left|x \cdot s\right|}\right)\right)}\]
Alternative 11
Error20.1
Cost52480
\[\frac{\sqrt[3]{\cos \left(x \cdot 2\right)} \cdot \sqrt[3]{\cos \left(x \cdot 2\right)}}{c \cdot c} \cdot \frac{\sqrt[3]{\cos \left(x \cdot 2\right)}}{{\left(\left|x \cdot s\right|\right)}^{2}}\]
Alternative 12
Error2.9
Cost52352
\[\left(\sqrt[3]{\cos \left(x \cdot 2\right)} \cdot \sqrt[3]{\cos \left(x \cdot 2\right)}\right) \cdot \frac{\sqrt[3]{\cos \left(x \cdot 2\right)}}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}\]
Alternative 13
Error27.8
Cost41408
\[\sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}} \cdot \left(\sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}} \cdot \sqrt[3]{\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}}\right)\]
Alternative 14
Error33.6
Cost39744
\[\frac{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}}{\sqrt{c \cdot \left|x \cdot s\right|} \cdot \sqrt{c \cdot \left|x \cdot s\right|}}\]
Alternative 15
Error22.1
Cost39616
\[\frac{\frac{\sqrt{\cos \left(x \cdot 2\right)}}{c} \cdot \frac{\sqrt{\cos \left(x \cdot 2\right)}}{\left|x \cdot s\right|}}{c \cdot \left|x \cdot s\right|}\]
Alternative 16
Error2.8
Cost39616
\[\frac{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}}{\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \left(\left|x \cdot s\right| \cdot \sqrt[3]{c}\right)}\]
Alternative 17
Error21.9
Cost39616
\[\frac{\sqrt{\cos \left(x \cdot 2\right)}}{c \cdot \left|x \cdot s\right|} \cdot \frac{\sqrt{\cos \left(x \cdot 2\right)}}{c \cdot \left|x \cdot s\right|}\]
Alternative 18
Error34.6
Cost39424
\[\frac{\sqrt{\cos \left(x \cdot 2\right)}}{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \frac{c}{\frac{\sqrt{\cos \left(x \cdot 2\right)}}{c}}}\]
Alternative 19
Error22.1
Cost39296
\[\frac{\sqrt{\cos \left(x \cdot 2\right)}}{\frac{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}{\sqrt{\cos \left(x \cdot 2\right)}}}\]
Alternative 20
Error3.4
Cost39296
\[\frac{\cos \left(x \cdot 2\right)}{{\left(\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \left(\left|x \cdot s\right| \cdot \sqrt[3]{c}\right)\right)}^{2}}\]
Alternative 21
Error33.6
Cost33088
\[\frac{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}}{\sqrt{c} \cdot \left(\left|x \cdot s\right| \cdot \sqrt{c}\right)}\]
Alternative 22
Error11.8
Cost33024
\[\frac{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}}{\sqrt[3]{{\left(c \cdot \left|x \cdot s\right|\right)}^{3}}}\]
Alternative 23
Error19.8
Cost33024
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(\sqrt{\left|x \cdot s\right|} \cdot {\left(\left|x \cdot s\right|\right)}^{1.5}\right)}\]
Alternative 24
Error11.8
Cost33024
\[\frac{\sqrt[3]{{\left(\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}\right)}^{3}}}{c \cdot \left|x \cdot s\right|}\]
Alternative 25
Error33.8
Cost32768
\[\frac{\cos \left(x \cdot 2\right)}{{\left(\sqrt{c} \cdot \left(\left|x \cdot s\right| \cdot \sqrt{c}\right)\right)}^{2}}\]
Alternative 26
Error21.8
Cost32704
\[\sqrt[3]{\frac{{\cos \left(x \cdot 2\right)}^{3}}{{\left(c \cdot \left|x \cdot s\right|\right)}^{6}}}\]
Alternative 27
Error44.2
Cost32704
\[e^{\log \cos \left(x \cdot 2\right) - 2 \cdot \log \left(c \cdot \left|x \cdot s\right|\right)}\]
Alternative 28
Error36.7
Cost32704
\[\frac{\cos \left(x \cdot 2\right)}{\sqrt[3]{{c}^{6} \cdot {\left(\left|x \cdot s\right|\right)}^{6}}}\]
Alternative 29
Error11.9
Cost32704
\[\frac{\cos \left(x \cdot 2\right)}{{\left(\sqrt[3]{{\left(c \cdot \left|x \cdot s\right|\right)}^{3}}\right)}^{2}}\]
Alternative 30
Error21.7
Cost32704
\[\sqrt[3]{{\left(\frac{\cos \left(x \cdot 2\right)}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}\right)}^{3}}\]
Alternative 31
Error27.8
Cost28096
\[\frac{\cos \left(x \cdot 2\right)}{\sqrt[3]{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)} \cdot \left(\sqrt[3]{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)} \cdot \sqrt[3]{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}\right)}\]
Alternative 32
Error29.9
Cost27584
\[\sqrt{\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}} \cdot \sqrt{\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}}\]
Alternative 33
Error27.8
Cost27584
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(\sqrt[3]{x \cdot \left(x \cdot \left(s \cdot s\right)\right)} \cdot \left(\sqrt[3]{x \cdot \left(x \cdot \left(s \cdot s\right)\right)} \cdot \sqrt[3]{x \cdot \left(x \cdot \left(s \cdot s\right)\right)}\right)\right)}\]
Alternative 34
Error27.7
Cost27584
\[\frac{\cos x \cdot \cos x}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)} - \frac{\sin x \cdot \sin x}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}\]
Alternative 35
Error27.8
Cost27328
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(\sqrt[3]{x \cdot \left(s \cdot s\right)} \cdot \left(\sqrt[3]{x \cdot \left(s \cdot s\right)} \cdot \sqrt[3]{x \cdot \left(s \cdot s\right)}\right)\right)\right)}\]
Alternative 36
Error27.8
Cost26816
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(s \cdot s\right) \cdot \sqrt[3]{x}\right)\right)\right)}\]
Alternative 37
Error46.1
Cost26432
\[e^{\log \left(\frac{\cos \left(x \cdot 2\right)}{c \cdot c}\right) - 2 \cdot \log \left(x \cdot s\right)}\]
Alternative 38
Error40.9
Cost26432
\[\frac{\cos \left(x \cdot 2\right)}{e^{2 \cdot \log \left(x \cdot s\right) + \log \left(c \cdot c\right)}}\]
Alternative 39
Error21.7
Cost26240
\[\frac{\cos \left(x \cdot 2\right)}{\sqrt[3]{{\left(c \cdot \left|x \cdot s\right|\right)}^{6}}}\]
Alternative 40
Error27.7
Cost20928
\[\frac{\cos \left(x \cdot 2\right)}{\sqrt{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)} \cdot \sqrt{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}}\]
Alternative 41
Error46.2
Cost20544
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(\sqrt{x \cdot \left(s \cdot s\right)} \cdot \sqrt{x \cdot \left(s \cdot s\right)}\right)\right)}\]
Alternative 42
Error2.6
Cost20288
\[\frac{\frac{1}{c} \cdot \frac{\cos \left(x \cdot 2\right)}{\left|x \cdot s\right|}}{c \cdot \left|x \cdot s\right|}\]
Alternative 43
Error43.3
Cost20288
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(\left(s \cdot \sqrt{x}\right) \cdot \left(s \cdot \sqrt{x}\right)\right)\right)}\]
Alternative 44
Error2.5
Cost20288
\[\frac{1}{c \cdot \left|x \cdot s\right|} \cdot \frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}\]
Alternative 45
Error46.9
Cost20224
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(\sqrt{x} \cdot \left(\left(s \cdot s\right) \cdot {x}^{1.5}\right)\right)}\]
Alternative 46
Error32.1
Cost20224
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \sqrt[3]{{\left(x \cdot \left(s \cdot s\right)\right)}^{3}}\right)}\]
Alternative 47
Error6.5
Cost20160
\[\frac{\frac{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}}{c}}{\left|x \cdot s\right|}\]
Alternative 48
Error6.7
Cost20160
\[\frac{\cos \left(x \cdot 2\right)}{\left|x \cdot s\right| \cdot \left(c \cdot \left(c \cdot \left|x \cdot s\right|\right)\right)}\]
Alternative 49
Error2.4
Cost20160
\[\frac{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}}{c \cdot \left|x \cdot s\right|}\]
Alternative 50
Error12.9
Cost20096
\[\frac{\frac{1}{c}}{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \frac{c}{\cos \left(x \cdot 2\right)}}\]
Alternative 51
Error12.9
Cost20096
\[\frac{\cos \left(x \cdot 2\right)}{c} \cdot \frac{\frac{1}{c}}{{\left(\left|x \cdot s\right|\right)}^{2}}\]
Alternative 52
Error12.9
Cost20096
\[\frac{1}{c} \cdot \frac{\frac{\cos \left(x \cdot 2\right)}{c}}{{\left(\left|x \cdot s\right|\right)}^{2}}\]
Alternative 53
Error20.0
Cost20096
\[\frac{1}{c \cdot c} \cdot \frac{\cos \left(x \cdot 2\right)}{{\left(\left|x \cdot s\right|\right)}^{2}}\]
Alternative 54
Error19.8
Cost20096
\[\frac{-\cos \left(x \cdot 2\right)}{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(-c \cdot c\right)}\]
Alternative 55
Error42.4
Cost20032
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot e^{2 \cdot \log \left(x \cdot s\right)}}\]
Alternative 56
Error27.7
Cost20032
\[\frac{\cos \left(x \cdot 2\right)}{{c}^{2} \cdot \left(x \cdot \left(x \cdot {s}^{2}\right)\right)}\]
Alternative 57
Error13.1
Cost19968
\[\frac{\cos \left(x \cdot 2\right)}{c \cdot \left(c \cdot {\left(\left|x \cdot s\right|\right)}^{2}\right)}\]
Alternative 58
Error19.9
Cost19968
\[\frac{\frac{\cos \left(x \cdot 2\right)}{c \cdot c}}{{\left(\left|x \cdot s\right|\right)}^{2}}\]
Alternative 59
Error19.8
Cost19968
\[\frac{\cos \left(x \cdot 2\right)}{{\left(\left|x \cdot s\right|\right)}^{2} \cdot \left(c \cdot c\right)}\]
Alternative 60
Error2.8
Cost19968
\[\cos \left(x \cdot 2\right) \cdot \frac{1}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}\]
Alternative 61
Error2.8
Cost19968
\[\frac{1}{\frac{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}{\cos \left(x \cdot 2\right)}}\]
Alternative 62
Error2.7
Cost19840
\[\frac{\cos \left(x \cdot 2\right)}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}\]
Alternative 63
Error16.3
Cost13632
\[\frac{\frac{1}{c \cdot \left|x \cdot s\right|}}{c \cdot \left|x \cdot s\right|}\]
Alternative 64
Error16.4
Cost13312
\[\frac{1}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}\]
Alternative 65
Error27.9
Cost7488
\[\frac{1}{c \cdot c} \cdot \frac{\cos \left(x \cdot 2\right)}{x \cdot \left(x \cdot \left(s \cdot s\right)\right)}\]
Alternative 66
Error31.3
Cost7360
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(\left(s \cdot s\right) \cdot \left(x \cdot x\right)\right)}\]
Alternative 67
Error19.8
Cost7360
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(\left(x \cdot s\right) \cdot \left(x \cdot s\right)\right)}\]
Alternative 68
Error21.6
Cost7360
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(s \cdot \left(x \cdot s\right)\right)\right)}\]
Alternative 69
Error22.8
Cost7360
\[\frac{\cos \left(x \cdot 2\right)}{c \cdot \left(c \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)\right)}\]
Alternative 70
Error27.7
Cost7360
\[\frac{\cos \left(x \cdot 2\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}\]
Alternative 71
Error27.9
Cost7360
\[\frac{\frac{\cos \left(x \cdot 2\right)}{c \cdot c}}{x \cdot \left(x \cdot \left(s \cdot s\right)\right)}\]
Alternative 72
Error26.2
Cost7360
\[\frac{\cos \left(x \cdot 2\right)}{\left(x \cdot \left(s \cdot s\right)\right) \cdot \left(x \cdot \left(c \cdot c\right)\right)}\]
Alternative 73
Error31.7
Cost832
\[\frac{1}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}\]
Alternative 74
Error61.5
Cost64
\[1\]
Alternative 75
Error32.5
Cost64
\[0\]
Alternative 76
Error62.2
Cost64
\[-1\]

Error

Derivation

  1. Initial program 27.7

    \[\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)}\]

  2. Simplified27.7

    \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt_binary64_42627.7

    \[\leadsto \frac{\cos \left(2 \cdot x\right)}{\left(c \cdot c\right) \cdot \color{blue}{\left(\sqrt{x \cdot \left(x \cdot \left(s \cdot s\right)\right)} \cdot \sqrt{x \cdot \left(x \cdot \left(s \cdot s\right)\right)}\right)}}\]

  5. Simplified27.7

    \[\leadsto \frac{\cos \left(2 \cdot x\right)}{\left(c \cdot c\right) \cdot \left(\color{blue}{\left|x \cdot s\right|} \cdot \sqrt{x \cdot \left(x \cdot \left(s \cdot s\right)\right)}\right)}\]

  6. Simplified19.8

    \[\leadsto \frac{\cos \left(2 \cdot x\right)}{\left(c \cdot c\right) \cdot \left(\left|x \cdot s\right| \cdot \color{blue}{\left|x \cdot s\right|}\right)}\]
  7. Using strategy rm

  8. Applied pow2_binary64_48519.8

    \[\leadsto \frac{\cos \left(2 \cdot x\right)}{\left(c \cdot c\right) \cdot \color{blue}{{\left(\left|x \cdot s\right|\right)}^{2}}}\]

  9. Applied pow2_binary64_48519.8

    \[\leadsto \frac{\cos \left(2 \cdot x\right)}{\color{blue}{{c}^{2}} \cdot {\left(\left|x \cdot s\right|\right)}^{2}}\]

  10. Applied pow-prod-down_binary64_4752.7

    \[\leadsto \frac{\cos \left(2 \cdot x\right)}{\color{blue}{{\left(c \cdot \left|x \cdot s\right|\right)}^{2}}}\]
  11. Using strategy rm

  12. Applied unpow2_binary64_4692.7

    \[\leadsto \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left(c \cdot \left|x \cdot s\right|\right) \cdot \left(c \cdot \left|x \cdot s\right|\right)}}\]

  13. Applied associate-/r*_binary64_3482.4

    \[\leadsto \color{blue}{\frac{\frac{\cos \left(2 \cdot x\right)}{c \cdot \left|x \cdot s\right|}}{c \cdot \left|x \cdot s\right|}}\]

  14. Simplified2.4

    \[\leadsto \frac{\color{blue}{\frac{\cos \left(x \cdot 2\right)}{c \cdot \left|x \cdot s\right|}}}{c \cdot \left|x \cdot s\right|}\]
  15. Using strategy rm

  16. Applied associate-/r*_binary64_3482.4

    \[\leadsto \frac{\color{blue}{\frac{\frac{\cos \left(x \cdot 2\right)}{c}}{\left|x \cdot s\right|}}}{c \cdot \left|x \cdot s\right|}\]

  17. Simplified2.4

    \[\leadsto \color{blue}{\frac{\frac{\frac{\cos \left(x \cdot 2\right)}{c}}{\left|x \cdot s\right|}}{c \cdot \left|x \cdot s\right|}}\]

  18. Final simplification2.4

    \[\leadsto \frac{\frac{\frac{\cos \left(x \cdot 2\right)}{c}}{\left|x \cdot s\right|}}{c \cdot \left|x \cdot s\right|}\]

Reproduce

herbie shell --seed 2021042 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))