Average Error: 24.0 → 11.6
Time: 3.4m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\alpha \le 1.1233087712068977 \cdot 10^{+224}:\\ \;\;\;\;\frac{\frac{\frac{{\left({1.0}^{3}\right)}^{3} + {\left({\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)}^{3}\right)}^{3}}{\left({1.0}^{3} \cdot {1.0}^{3} - {1.0}^{3} \cdot {\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)}^{3}\right) + {\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)}^{3} \cdot {\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)}^{3}}}{\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right) \cdot \left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right) + \left(1.0 \cdot 1.0 - 1.0 \cdot \sqrt[3]{\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right) \cdot \left(\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right) \cdot \left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)\right)}\right)}}{2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2.0}{\alpha} + \frac{\frac{8.0}{\alpha} - 4.0}{\alpha \cdot \alpha}}{2.0}\\ \end{array}\]

Error

Bits error versus alpha

Bits error versus beta

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if alpha < 1.1233087712068977e+224

    1. Initial program 20.0

      \[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity20.0

      \[\leadsto \frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\color{blue}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)}} + 1.0}{2.0}\]

    4. Applied *-un-lft-identity20.0

      \[\leadsto \frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\color{blue}{1 \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)} + 1.0}{2.0}\]

    5. Applied times-frac8.5

      \[\leadsto \frac{\frac{\color{blue}{\frac{\alpha + \beta}{1} \cdot \frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0\right)} + 1.0}{2.0}\]

    6. Applied times-frac8.4

      \[\leadsto \frac{\color{blue}{\frac{\frac{\alpha + \beta}{1}}{1} \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}} + 1.0}{2.0}\]

    7. Simplified8.4

      \[\leadsto \frac{\color{blue}{\left(\beta + \alpha\right)} \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
    8. Using strategy rm

    9. Applied flip3-+8.5

      \[\leadsto \frac{\color{blue}{\frac{{\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)}^{3} + {1.0}^{3}}{\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right) + \left(1.0 \cdot 1.0 - \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right) \cdot 1.0\right)}}}{2.0}\]
    10. Using strategy rm

    11. Applied add-cbrt-cube8.5

      \[\leadsto \frac{\frac{{\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)}^{3} + {1.0}^{3}}{\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right) + \left(1.0 \cdot 1.0 - \color{blue}{\sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)}} \cdot 1.0\right)}}{2.0}\]
    12. Using strategy rm

    13. Applied flip3-+8.5

      \[\leadsto \frac{\frac{\color{blue}{\frac{{\left({\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)}^{3}\right)}^{3} + {\left({1.0}^{3}\right)}^{3}}{{\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)}^{3} \cdot {\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)}^{3} + \left({1.0}^{3} \cdot {1.0}^{3} - {\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)}^{3} \cdot {1.0}^{3}\right)}}}{\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right) + \left(1.0 \cdot 1.0 - \sqrt[3]{\left(\left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)\right) \cdot \left(\left(\beta + \alpha\right) \cdot \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0}\right)} \cdot 1.0\right)}}{2.0}\]

    if 1.1233087712068977e+224 < alpha

    1. Initial program 63.2

      \[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]

    2. Taylor expanded around inf 43.1

      \[\leadsto \frac{\color{blue}{\left(2.0 \cdot \frac{1}{\alpha} + 8.0 \cdot \frac{1}{{\alpha}^{3}}\right) - 4.0 \cdot \frac{1}{{\alpha}^{2}}}}{2.0}\]

    3. Simplified43.1

      \[\leadsto \frac{\color{blue}{\frac{2.0}{\alpha} + \frac{\frac{8.0}{\alpha} - 4.0}{\alpha \cdot \alpha}}}{2.0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification11.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\alpha \le 1.1233087712068977 \cdot 10^{+224}:\\ \;\;\;\;\frac{\frac{\frac{{\left({1.0}^{3}\right)}^{3} + {\left({\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)}^{3}\right)}^{3}}{\left({1.0}^{3} \cdot {1.0}^{3} - {1.0}^{3} \cdot {\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)}^{3}\right) + {\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)}^{3} \cdot {\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)}^{3}}}{\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right) \cdot \left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right) + \left(1.0 \cdot 1.0 - 1.0 \cdot \sqrt[3]{\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right) \cdot \left(\left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right) \cdot \left(\frac{\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2 \cdot i}}{2.0 + \left(\left(\beta + \alpha\right) + 2 \cdot i\right)} \cdot \left(\beta + \alpha\right)\right)\right)}\right)}}{2.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2.0}{\alpha} + \frac{\frac{8.0}{\alpha} - 4.0}{\alpha \cdot \alpha}}{2.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/2"
  :pre (and (> alpha -1) (> beta -1) (> i 0))
  (/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0))

Details

Time bar (total: 3.3m)Debug log

start177.0ms

Algorithm
intervals

setup906.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize30.0ms

Local error

Found 4 expressions with local error:

24.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(+ (+ alpha beta) (* 2 i))

rewrite154.0ms

Algorithm
rewrite-expression-head
Counts
4 → 111
Calls

4 calls. Slowest were:

80.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
45.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
19.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series508.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

241.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
196.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
52.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
20.0ms
(+ (+ alpha beta) (* 2 i))

simplify15.9s

Counts
111 → 123
Calls

111 calls. Slowest were:

687.0ms
(/ (/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
541.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
540.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

localize31.0ms

Local error

Found 4 expressions with local error:

4.6b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.2b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Counts
4 → 197
Calls

4 calls. Slowest were:

45.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
25.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
23.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series475.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

190.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
141.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
101.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
43.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify28.2s

Counts
224 → 209
Calls

224 calls. Slowest were:

724.0ms
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
715.0ms
(* (+ (pow beta 3) (pow alpha 3)) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
651.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

prune3.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize65.0ms

Local error

Found 4 expressions with local error:

4.6b
(+ (pow (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3) (pow 1.0 3))
3.1b
(- (* 1.0 1.0) (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
2.2b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.2b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Counts
4 → 174
Calls

4 calls. Slowest were:

43.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
42.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
9.0ms
(+ (pow (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3) (pow 1.0 3))

series8.4s

Counts
4 → 12
Calls

4 calls. Slowest were:

7.7s
(+ (pow (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3) (pow 1.0 3))
295.0ms
(- (* 1.0 1.0) (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
264.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
199.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify27.3s

Counts
152 → 186
Calls

152 calls. Slowest were:

699.0ms
(* (- (* beta beta) (* alpha alpha)) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
654.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
579.0ms
(* (+ (pow beta 3) (pow alpha 3)) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

prune5.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize56.0ms

Local error

Found 4 expressions with local error:

10.8b
(cbrt (* (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
4.6b
(+ (pow (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3) (pow 1.0 3))
3.1b
(- (* 1.0 1.0) (* (cbrt (* (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0))
2.2b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite311.0ms

Algorithm
rewrite-expression-head
Counts
4 → 325
Calls

4 calls. Slowest were:

250.0ms
(cbrt (* (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
32.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
5.0ms
(+ (pow (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3) (pow 1.0 3))

series7.6s

Counts
4 → 12
Calls

4 calls. Slowest were:

7.0s
(+ (pow (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3) (pow 1.0 3))
268.0ms
(- (* 1.0 1.0) (* (cbrt (* (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0))
209.0ms
(cbrt (* (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
155.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify1.4m

Counts
302 → 337
Calls

302 calls. Slowest were:

739.0ms
(cbrt (* (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (* (+ (pow beta 3) (pow alpha 3)) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
647.0ms
(* (- (* beta beta) (* alpha alpha)) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
633.0ms
(cbrt (* (* (* (+ (pow beta 3) (pow alpha 3)) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (* (- (* beta beta) (* alpha alpha)) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))

prune10.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

regimes455.0ms

Accuracy

11% (5.8b remaining)

Error of 11.6b against oracle of 5.9b and baseline of 12.4b

bsearch250.0ms