Average Error: 52.5 → 37.5
Time: 2.6m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\alpha \le 8.87465568757806 \cdot 10^{+151}:\\ \;\;\;\;\frac{\sqrt{\left(i + \beta\right) \cdot \left(i + \alpha\right)} \cdot \frac{\sqrt{\left(i + \beta\right) \cdot \left(i + \alpha\right)}}{\sqrt{\left(2 \cdot i + \left(\alpha + \beta\right)\right) \cdot \left(2 \cdot i + \left(\alpha + \beta\right)\right) - 1.0}}}{\frac{\left(2 \cdot i + \left(\alpha + \beta\right)\right) \cdot \left(2 \cdot i + \left(\alpha + \beta\right)\right)}{\frac{i \cdot i + i \cdot \left(\alpha + \beta\right)}{\sqrt{\left(2 \cdot i + \left(\alpha + \beta\right)\right) \cdot \left(2 \cdot i + \left(\alpha + \beta\right)\right) - 1.0}}}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

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 < 8.87465568757806e+151

    1. Initial program 50.3

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

    2. Initial simplification50.3

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

    4. Applied add-sqr-sqrt50.3

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

    5. Applied times-frac35.1

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

    6. Applied associate-/l*35.1

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

    7. Simplified35.1

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

    9. Applied *-un-lft-identity35.1

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

    10. Applied add-sqr-sqrt35.1

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

    11. Applied times-frac35.1

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

    12. Simplified35.1

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

    13. Simplified35.1

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

    if 8.87465568757806e+151 < alpha

    1. Initial program 62.5

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

    2. Initial simplification62.5

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

    3. Taylor expanded around inf 48.0

      \[\leadsto \color{blue}{0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification37.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\alpha \le 8.87465568757806 \cdot 10^{+151}:\\ \;\;\;\;\frac{\sqrt{\left(i + \beta\right) \cdot \left(i + \alpha\right)} \cdot \frac{\sqrt{\left(i + \beta\right) \cdot \left(i + \alpha\right)}}{\sqrt{\left(2 \cdot i + \left(\alpha + \beta\right)\right) \cdot \left(2 \cdot i + \left(\alpha + \beta\right)\right) - 1.0}}}{\frac{\left(2 \cdot i + \left(\alpha + \beta\right)\right) \cdot \left(2 \cdot i + \left(\alpha + \beta\right)\right)}{\frac{i \cdot i + i \cdot \left(\alpha + \beta\right)}{\sqrt{\left(2 \cdot i + \left(\alpha + \beta\right)\right) \cdot \left(2 \cdot i + \left(\alpha + \beta\right)\right) - 1.0}}}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/4"
  :pre (and (> alpha -1) (> beta -1) (> i 1))
  (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))

Details

Time bar (total: 2.6m)Debug log

start71.0ms

Algorithm
intervals

setup706.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.4b

localize57.0ms

Local error

Found 4 expressions with local error:

44.6b
(/ (* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i))) (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))
33.1b
(/ (/ (* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i))) (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0)) (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))))
0.1b
(* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i)))
0.0b
(* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Counts
4 → 163
Calls

4 calls. Slowest were:

54.0ms
(/ (/ (* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i))) (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0)) (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))))
41.0ms
(/ (* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i))) (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))
22.0ms
(* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i)))

series1.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

567.0ms
(/ (* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i))) (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))
297.0ms
(/ (/ (* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i))) (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0)) (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))))
121.0ms
(* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i)))
39.0ms
(* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta)))

simplify32.5s

Counts
164 → 175
Calls

164 calls. Slowest were:

965.0ms
(/ (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (* (cbrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0)) (cbrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))))
854.0ms
(* (+ (pow (* 2 i) 3) (pow (+ alpha beta) 3)) (+ (pow (* 2 i) 3) (pow (+ alpha beta) 3)))
777.0ms
(/ (* (* (/ (* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i))) (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0)) (/ (* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i))) (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))) (/ (* (+ (* (+ alpha beta) i) (+ (* i i) (* beta alpha))) (+ (* (+ alpha beta) i) (* i i))) (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))) (* (* (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta)))) (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta)))))

prune3.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 32.9b

localize55.0ms

Local error

Found 4 expressions with local error:

38.8b
(/ (* (+ i (+ beta alpha)) i) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))
33.1b
(/ (* (* (+ beta i) (+ i alpha)) (/ (* (+ i (+ beta alpha)) i) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))) (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))))
5.7b
(* (* (+ beta i) (+ i alpha)) (/ (* (+ i (+ beta alpha)) i) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0)))
0.0b
(* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta)))

rewrite473.0ms

Algorithm
rewrite-expression-head
Counts
4 → 156
Calls

4 calls. Slowest were:

407.0ms
(* (* (+ beta i) (+ i alpha)) (/ (* (+ i (+ beta alpha)) i) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0)))
27.0ms
(/ (* (* (+ beta i) (+ i alpha)) (/ (* (+ i (+ beta alpha)) i) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))) (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))))
18.0ms
(* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta)))

series1.5s

Counts
4 → 12
Calls

4 calls. Slowest were:

929.0ms
(/ (* (* (+ beta i) (+ i alpha)) (/ (* (+ i (+ beta alpha)) i) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))) (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))))
430.0ms
(* (* (+ beta i) (+ i alpha)) (/ (* (+ i (+ beta alpha)) i) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0)))
133.0ms
(/ (* (+ i (+ beta alpha)) i) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))
55.0ms
(* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta)))

simplify29.5s

Counts
147 → 168
Calls

147 calls. Slowest were:

1.1s
(* (- i alpha) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))
804.0ms
(* (+ (pow (* 2 i) 3) (pow (+ alpha beta) 3)) (+ (pow (* 2 i) 3) (pow (+ alpha beta) 3)))
713.0ms
(* (- beta i) (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))

prune3.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 32.9b

localize29.0ms

Local error

Found 4 expressions with local error:

37.2b
(sqrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))
37.2b
(sqrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))
32.7b
(/ (+ (* i (+ i alpha)) (* beta (+ i alpha))) (sqrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0)))
32.5b
(/ (+ (* (+ alpha beta) i) (* i i)) (sqrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Counts
4 → 132
Calls

4 calls. Slowest were:

44.0ms
(/ (+ (* (+ alpha beta) i) (* i i)) (sqrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0)))
42.0ms
(/ (+ (* i (+ i alpha)) (* beta (+ i alpha))) (sqrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0)))
21.0ms
(sqrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))

series986.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

378.0ms
(/ (+ (* (+ alpha beta) i) (* i i)) (sqrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0)))
370.0ms
(/ (+ (* i (+ i alpha)) (* beta (+ i alpha))) (sqrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0)))
123.0ms
(sqrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))
115.0ms
(sqrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))

simplify1.0m

Counts
153 → 144
Calls

153 calls. Slowest were:

1.0s
(/ (cbrt (+ (* i (+ i alpha)) (* beta (+ i alpha)))) (cbrt (sqrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0))))
808.0ms
(/ (+ i alpha) (sqrt (* (cbrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0)) (cbrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0)))))
729.0ms
(/ (cbrt (+ (* i (+ i alpha)) (* beta (+ i alpha)))) (sqrt (- (* (+ (* i 2) (+ beta alpha)) (+ (* i 2) (+ beta alpha))) 1.0)))

prune3.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 32.9b

localize42.0ms

Local error

Found 4 expressions with local error:

37.2b
(sqrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))
37.2b
(sqrt (- (* (+ (+ alpha beta) (* i 2)) (+ (+ alpha beta) (* i 2))) 1.0))
32.5b
(sqrt (* (+ i beta) (+ alpha i)))
32.5b
(sqrt (* (+ i beta) (+ alpha i)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Counts
4 → 62
Calls

4 calls. Slowest were:

23.0ms
(sqrt (- (* (+ (+ alpha beta) (* i 2)) (+ (+ alpha beta) (* i 2))) 1.0))
21.0ms
(sqrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))
3.0ms
(sqrt (* (+ i beta) (+ alpha i)))

series462.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

150.0ms
(sqrt (- (* (+ (+ alpha beta) (* i 2)) (+ (+ alpha beta) (* i 2))) 1.0))
119.0ms
(sqrt (- (* (+ (* 2 i) (+ alpha beta)) (+ (* 2 i) (+ alpha beta))) 1.0))
98.0ms
(sqrt (* (+ i beta) (+ alpha i)))
96.0ms
(sqrt (* (+ i beta) (+ alpha i)))

simplify9.5s

Counts
42 → 74
Calls

42 calls. Slowest were:

634.0ms
(sqrt (sqrt (- (* (+ (+ alpha beta) (* i 2)) (+ (+ alpha beta) (* i 2))) 1.0)))
619.0ms
(sqrt (* (+ i beta) (- (* alpha alpha) (* i i))))
572.0ms
(sqrt (- (* (+ (+ alpha beta) (* i 2)) (+ (+ alpha beta) (* i 2))) 1.0))

prune2.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 32.9b

regimes281.0ms

Accuracy

53.1% (1.3b remaining)

Error of 37.5b against oracle of 36.1b and baseline of 39.0b

bsearch137.0ms