Average Error: 30.0 → 0.9
Time: 4.3m
Precision: 64
Internal Precision: 128
\[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 342.69244116077795:\\ \;\;\;\;\frac{\left(\frac{\sqrt{\sqrt[3]{{\left(2 + \frac{2}{3} \cdot {x}^{3}\right)}^{3} - {\left({x}^{2}\right)}^{3}}}}{\sqrt{\sqrt{\left(\left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot {x}^{2} + {x}^{2} \cdot {x}^{2}\right) + \left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot \left(2 + \frac{2}{3} \cdot {x}^{3}\right)}}} \cdot \frac{\sqrt{\sqrt[3]{{\left(2 + \frac{2}{3} \cdot {x}^{3}\right)}^{3} - {\left({x}^{2}\right)}^{3}}}}{\sqrt{\sqrt{\left(\left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot {x}^{2} + {x}^{2} \cdot {x}^{2}\right) + \left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot \left(2 + \frac{2}{3} \cdot {x}^{3}\right)}}}\right) \cdot \frac{\sqrt[3]{{\left(2 + \frac{2}{3} \cdot {x}^{3}\right)}^{3} - {\left({x}^{2}\right)}^{3}} \cdot \sqrt[3]{{\left(2 + \frac{2}{3} \cdot {x}^{3}\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\sqrt{\left(\left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot {x}^{2} + {x}^{2} \cdot {x}^{2}\right) + \left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot \left(2 + \frac{2}{3} \cdot {x}^{3}\right)}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{\left(e^{\left(1 - \varepsilon\right) \cdot \left(-x\right)} \cdot \left(1 + \frac{1}{\varepsilon}\right)\right) \cdot \left(\left(e^{\left(1 - \varepsilon\right) \cdot \left(-x\right)} \cdot \left(1 + \frac{1}{\varepsilon}\right)\right) \cdot \left(e^{\left(1 - \varepsilon\right) \cdot \left(-x\right)} \cdot \left(1 + \frac{1}{\varepsilon}\right)\right)\right)} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{\left(-x\right) \cdot \left(\varepsilon + 1\right)}}{2}\\ \end{array}\]

Error

Bits error versus x

Bits error versus eps

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < 342.69244116077795

    1. Initial program 39.5

      \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]

    2. Taylor expanded around 0 1.1

      \[\leadsto \frac{\color{blue}{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) - {x}^{2}}}{2}\]
    3. Using strategy rm

    4. Applied flip3--1.1

      \[\leadsto \frac{\color{blue}{\frac{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}}}{2}\]
    5. Using strategy rm

    6. Applied add-sqr-sqrt1.1

      \[\leadsto \frac{\frac{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}{\color{blue}{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)} \cdot \sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}}}}{2}\]

    7. Applied add-cube-cbrt1.1

      \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}} \cdot \sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}\right) \cdot \sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}}{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)} \cdot \sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}}}{2}\]

    8. Applied times-frac1.2

      \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}} \cdot \sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}} \cdot \frac{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}}}}{2}\]
    9. Using strategy rm

    10. Applied add-sqr-sqrt1.2

      \[\leadsto \frac{\frac{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}} \cdot \sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}} \cdot \frac{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\sqrt{\color{blue}{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)} \cdot \sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}}}}}{2}\]

    11. Applied sqrt-prod2.7

      \[\leadsto \frac{\frac{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}} \cdot \sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}} \cdot \frac{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\color{blue}{\sqrt{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}} \cdot \sqrt{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}}}}}{2}\]

    12. Applied add-sqr-sqrt1.2

      \[\leadsto \frac{\frac{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}} \cdot \sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}} \cdot \frac{\color{blue}{\sqrt{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}} \cdot \sqrt{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}}}{\sqrt{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}} \cdot \sqrt{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}}}}{2}\]

    13. Applied times-frac1.2

      \[\leadsto \frac{\frac{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}} \cdot \sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}} \cdot \color{blue}{\left(\frac{\sqrt{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}}{\sqrt{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}}} \cdot \frac{\sqrt{\sqrt[3]{{\left(\frac{2}{3} \cdot {x}^{3} + 2\right)}^{3} - {\left({x}^{2}\right)}^{3}}}}{\sqrt{\sqrt{\left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot \left(\frac{2}{3} \cdot {x}^{3} + 2\right) + \left({x}^{2} \cdot {x}^{2} + \left(\frac{2}{3} \cdot {x}^{3} + 2\right) \cdot {x}^{2}\right)}}}\right)}}{2}\]

    if 342.69244116077795 < x

    1. Initial program 0

      \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
    2. Using strategy rm

    3. Applied add-cbrt-cube0

      \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x}\right) \cdot \left(\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x}\right)\right) \cdot \left(\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x}\right)}} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 342.69244116077795:\\ \;\;\;\;\frac{\left(\frac{\sqrt{\sqrt[3]{{\left(2 + \frac{2}{3} \cdot {x}^{3}\right)}^{3} - {\left({x}^{2}\right)}^{3}}}}{\sqrt{\sqrt{\left(\left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot {x}^{2} + {x}^{2} \cdot {x}^{2}\right) + \left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot \left(2 + \frac{2}{3} \cdot {x}^{3}\right)}}} \cdot \frac{\sqrt{\sqrt[3]{{\left(2 + \frac{2}{3} \cdot {x}^{3}\right)}^{3} - {\left({x}^{2}\right)}^{3}}}}{\sqrt{\sqrt{\left(\left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot {x}^{2} + {x}^{2} \cdot {x}^{2}\right) + \left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot \left(2 + \frac{2}{3} \cdot {x}^{3}\right)}}}\right) \cdot \frac{\sqrt[3]{{\left(2 + \frac{2}{3} \cdot {x}^{3}\right)}^{3} - {\left({x}^{2}\right)}^{3}} \cdot \sqrt[3]{{\left(2 + \frac{2}{3} \cdot {x}^{3}\right)}^{3} - {\left({x}^{2}\right)}^{3}}}{\sqrt{\left(\left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot {x}^{2} + {x}^{2} \cdot {x}^{2}\right) + \left(2 + \frac{2}{3} \cdot {x}^{3}\right) \cdot \left(2 + \frac{2}{3} \cdot {x}^{3}\right)}}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{\left(e^{\left(1 - \varepsilon\right) \cdot \left(-x\right)} \cdot \left(1 + \frac{1}{\varepsilon}\right)\right) \cdot \left(\left(e^{\left(1 - \varepsilon\right) \cdot \left(-x\right)} \cdot \left(1 + \frac{1}{\varepsilon}\right)\right) \cdot \left(e^{\left(1 - \varepsilon\right) \cdot \left(-x\right)} \cdot \left(1 + \frac{1}{\varepsilon}\right)\right)\right)} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{\left(-x\right) \cdot \left(\varepsilon + 1\right)}}{2}\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 
(FPCore (x eps)
  :name "NMSE Section 6.1 mentioned, A"
  (/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2))

Details

Time bar (total: 4.0m)Debug log

start907.0ms

Algorithm
intervals

setup242.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.9b

localize48.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))
0.0b
(* (- 1 eps) x)
0.0b
(* (+ 1 eps) x)
0.0b
(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Counts
4 → 145
Calls

4 calls. Slowest were:

25.0ms
(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))
14.0ms
(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
5.0ms
(* (- 1 eps) x)

series202.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

144.0ms
(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))
27.0ms
(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
19.0ms
(* (- 1 eps) x)
13.0ms
(* (+ 1 eps) x)

simplify49.4s

Counts
204 → 157
Calls

204 calls. Slowest were:

746.0ms
(* (- 1 (/ 1 eps)) (+ (* (/ 1 eps) (/ 1 eps)) (+ (* 1 1) (* (/ 1 eps) 1))))
650.0ms
(* (* (* (+ 1 (/ 1 eps)) (+ 1 (/ 1 eps))) (+ 1 (/ 1 eps))) (* (* (exp (- (* (- 1 eps) x))) (exp (- (* (- 1 eps) x)))) (exp (- (* (- 1 eps) x)))))
630.0ms
(* (exp (* (- 1 eps) x)) (+ (* (/ 1 eps) (/ 1 eps)) (+ (* 1 1) (* (/ 1 eps) 1))))

prune2.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

8.0b
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
0.1b
(* 2/3 (pow x 3))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

15.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
1.0ms
(* 2/3 (pow x 3))

series52.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

26.0ms
(* 2/3 (pow x 3))
25.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

simplify495.0ms

Counts
17 → 35
Calls

17 calls. Slowest were:

130.0ms
(/ (exp (+ (* 2/3 (pow x 3)) 2)) (exp (pow x 2)))
85.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
74.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune507.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

13.4b
(/ (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3)) (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2)))))
12.4b
(- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))
0.1b
(* (pow x 2) (pow x 2))
0.1b
(pow (pow x 2) 3)

rewrite155.0ms

Algorithm
rewrite-expression-head
Counts
4 → 211
Calls

4 calls. Slowest were:

116.0ms
(/ (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3)) (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2)))))
31.0ms
(- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))
3.0ms
(* (pow x 2) (pow x 2))

series173.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

62.0ms
(/ (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3)) (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2)))))
54.0ms
(- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))
31.0ms
(pow (pow x 2) 3)
24.0ms
(* (pow x 2) (pow x 2))

simplify53.8s

Counts
269 → 223
Calls

269 calls. Slowest were:

750.0ms
(/ (- (pow (sqrt (+ (* 2/3 (pow x 3)) 2)) 3) (pow x 3)) (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))
602.0ms
(/ (+ (sqrt (pow (+ (* 2/3 (pow x 3)) 2) 3)) (sqrt (pow (pow x 2) 3))) (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))
600.0ms
(/ (- (sqrt (pow (+ (* 2/3 (pow x 3)) 2) 3)) (sqrt (pow (pow x 2) 3))) (cbrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))

prune3.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

12.7b
(/ (* (cbrt (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))) (cbrt (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3)))) (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))
12.4b
(/ (cbrt (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))) (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))
12.4b
(- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))
12.4b
(- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))

rewrite199.0ms

Algorithm
rewrite-expression-head
Counts
4 → 346
Calls

4 calls. Slowest were:

65.0ms
(/ (cbrt (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))) (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))
59.0ms
(/ (* (cbrt (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))) (cbrt (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3)))) (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))
36.0ms
(- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))

series385.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

154.0ms
(/ (cbrt (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))) (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))
146.0ms
(/ (* (cbrt (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))) (cbrt (- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3)))) (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))
45.0ms
(- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))
39.0ms
(- (pow (+ (* 2/3 (pow x 3)) 2) 3) (pow (pow x 2) 3))

simplify1.9m

Counts
523 → 358
Calls

523 calls. Slowest were:

929.0ms
(/ (cbrt (+ (sqrt (pow (+ (* 2/3 (pow x 3)) 2) 3)) (pow x 3))) (sqrt (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2)))))))
823.0ms
(/ (cbrt (- (pow (sqrt (+ (* 2/3 (pow x 3)) 2)) 3) (pow x 3))) (sqrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))
681.0ms
(sqrt (cbrt (+ (* (+ (* 2/3 (pow x 3)) 2) (+ (* 2/3 (pow x 3)) 2)) (+ (* (pow x 2) (pow x 2)) (* (+ (* 2/3 (pow x 3)) 2) (pow x 2))))))

prune8.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

regimes142.0ms

Accuracy

97% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.1b

bsearch604.0ms