Average Error: 52.9 → 37.9
Time: 4.8m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\beta \le 1.4918065531878475 \cdot 10^{+151}:\\ \;\;\;\;\frac{i \cdot \left(i + \left(\beta + \alpha\right)\right)}{\left(\left(\beta + \alpha\right) + 2 \cdot i\right) \cdot \left(\left(\beta + \alpha\right) + 2 \cdot i\right) - 1.0} \cdot \frac{\alpha \cdot \left(i + \beta\right) + \left(i + \beta\right) \cdot i}{\left(\left(\beta + \alpha\right) + 2 \cdot i\right) \cdot \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

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 beta < 1.4918065531878475e+151

    1. Initial program 50.8

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

    3. Applied times-frac35.5

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

    4. Applied associate-/l*35.5

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

    6. Applied div-inv35.6

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

    7. Applied div-inv35.5

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

    8. Applied times-frac35.5

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

    9. Simplified35.5

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

    if 1.4918065531878475e+151 < beta

    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. Taylor expanded around inf 49.0

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

  4. Final simplification37.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\beta \le 1.4918065531878475 \cdot 10^{+151}:\\ \;\;\;\;\frac{i \cdot \left(i + \left(\beta + \alpha\right)\right)}{\left(\left(\beta + \alpha\right) + 2 \cdot i\right) \cdot \left(\left(\beta + \alpha\right) + 2 \cdot i\right) - 1.0} \cdot \frac{\alpha \cdot \left(i + \beta\right) + \left(i + \beta\right) \cdot i}{\left(\left(\beta + \alpha\right) + 2 \cdot i\right) \cdot \left(\left(\beta + \alpha\right) + 2 \cdot i\right)}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019021 
(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: 4.8m)Debug log

sample68.0ms

Algorithm
intervals
Results
41.0ms256×body80valid
10.0ms256×pre80true

simplify228.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
227.0ms
(/ (/ (* (* 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))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.5b

localize41.0ms

Local error

Found 4 expressions with local error:

47.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
37.3b
(/ (/ (* (* 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))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
48×flip-+
48×flip3-+
44×times-frac
42×associate-/r/
38×add-exp-log
38×add-cbrt-cube
32×frac-times
28×associate-*r/
25×add-cube-cbrt
25×*-un-lft-identity
25×add-sqr-sqrt
16×associate-*l/
14×associate-/l*
13×div-exp
13×cbrt-undiv
11×pow1
10×cbrt-unprod
10×prod-exp
9×associate-/l/
6×div-inv
6×associate-*r*
4×add-log-exp
4×associate-*l*
4×associate-/r*
2×*-commutative
2×pow-prod-down
2×distribute-lft-in
2×frac-2neg
2×clear-num
2×distribute-rgt-in
1×flip--
1×pow-prod-up
1×flip3--
1×pow-plus
1×pow2
Counts
4 → 170
Calls
4 calls:
Slowest
49.0ms
(/ (/ (* (* 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))
37.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
17.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
11.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
759.0ms
(/ (/ (* (* 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))
172.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
71.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
49.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify38.6s

Counts
191 → 182
Calls
191 calls:
Slowest
873.0ms
(- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)
751.0ms
(* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))
745.0ms
(* (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))
680.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))) (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
639.0ms
(/ (* (* (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))) (/ (* (* 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) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 37.2b

localize21.0ms

Local error

Found 4 expressions with local error:

35.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
34.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
29.4b
(/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
6.6b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
1416×times-frac
530×add-cube-cbrt
530×*-un-lft-identity
530×add-sqr-sqrt
186×associate-/r/
99×div-inv
89×flip-+
89×flip3-+
71×associate-/r*
34×add-exp-log
34×add-cbrt-cube
20×div-exp
20×cbrt-undiv
16×associate-/l*
7×associate-/l/
4×add-log-exp
4×frac-2neg
4×clear-num
4×pow1
2×associate-*r/
1×flip--
1×div-sub
1×flip3--
Counts
4 → 668
Calls
4 calls:
Slowest
51.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
42.0ms
(/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
19.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
8.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
836.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
493.0ms
(/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
82.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
51.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify3.1m

Counts
1143 → 680
Calls
1143 calls:
Slowest
938.0ms
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
934.0ms
(/ (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (+ (+ alpha beta) (* 2 i)))))
902.0ms
(/ (/ i 1) (/ (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) 1))
829.0ms
(/ (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (cbrt (+ (+ alpha beta) (* 2 i)))))
682.0ms
(/ (/ (* (* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))) (/ (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))))

prune11.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 37.1b

localize19.0ms

Local error

Found 4 expressions with local error:

40.7b
(/ (+ (* (+ i beta) i) (* alpha (+ i beta))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
40.7b
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
0.2b
(* (/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (/ (+ (* (+ i beta) i) (* alpha (+ i beta))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))))
0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
34×add-cbrt-cube
24×flip-+
24×flip3-+
20×associate-/r/
18×associate-*r*
14×add-cube-cbrt
14×*-un-lft-identity
14×add-sqr-sqrt
13×associate-*r/
13×frac-times
12×associate-*l*
12×times-frac
11×associate-*l/
11×pow1
10×cbrt-unprod
10×prod-exp
10×div-exp
10×cbrt-undiv
8×associate-/l/
4×add-log-exp
4×associate-/l*
4×div-inv
4×frac-add
4×associate-/r*
2×flip--
2×*-commutative
2×pow-prod-down
2×flip3--
2×frac-2neg
2×clear-num
1×pow-prod-up
1×pow-plus
1×distribute-lft-in
1×distribute-rgt-in
1×pow2
Counts
4 → 136
Calls
4 calls:
Slowest
48.0ms
(* (/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (/ (+ (* (+ i beta) i) (* alpha (+ i beta))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))))
35.0ms
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
31.0ms
(/ (+ (* (+ i beta) i) (* alpha (+ i beta))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
23.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

series974.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
710.0ms
(* (/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (/ (+ (* (+ i beta) i) (* alpha (+ i beta))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))))
141.0ms
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
82.0ms
(/ (+ (* (+ i beta) i) (* alpha (+ i beta))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
42.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify22.3s

Counts
119 → 148
Calls
119 calls:
Slowest
905.0ms
(/ i (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
903.0ms
(* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))
730.0ms
(+ (* (* (- (* i i) (* beta beta)) i) (- i beta)) (* (- i beta) (* alpha (- (* i i) (* beta beta)))))
610.0ms
(/ (+ (+ alpha beta) i) (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
609.0ms
(* (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 37.1b

localize53.0ms

Local error

Found 4 expressions with local error:

40.7b
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
35.4b
(sqrt (+ (* (+ i beta) i) (* alpha (+ i beta))))
35.4b
(sqrt (* (+ i alpha) (+ beta i)))
0.4b
(/ (sqrt (* (+ i alpha) (+ beta i))) (+ (* 2 i) (+ beta alpha)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
22×sqrt-div
19×flip-+
19×flip3-+
17×add-sqr-sqrt
16×add-cube-cbrt
16×*-un-lft-identity
15×times-frac
10×associate-/l/
10×associate-*r/
8×sqrt-prod
8×add-exp-log
8×associate-*l/
8×add-cbrt-cube
8×frac-times
6×associate-/r*
5×associate-/l*
4×add-log-exp
4×associate-/r/
4×frac-add
4×pow1
2×div-inv
2×div-exp
2×pow1/2
2×frac-2neg
2×clear-num
2×cbrt-undiv
1×flip--
1×flip3--
1×rem-sqrt-square
Counts
4 → 99
Calls
4 calls:
Slowest
20.0ms
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
12.0ms
(/ (sqrt (* (+ i alpha) (+ beta i))) (+ (* 2 i) (+ beta alpha)))
4.0ms
(sqrt (+ (* (+ i beta) i) (* alpha (+ i beta))))
1.0ms
(sqrt (* (+ i alpha) (+ beta i)))

series373.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(/ (* i (+ (+ alpha beta) i)) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
87.0ms
(sqrt (+ (* (+ i beta) i) (* alpha (+ i beta))))
82.0ms
(/ (sqrt (* (+ i alpha) (+ beta i))) (+ (* 2 i) (+ beta alpha)))
82.0ms
(sqrt (* (+ i alpha) (+ beta i)))

simplify15.0s

Counts
88 → 111
Calls
88 calls:
Slowest
709.0ms
(sqrt (+ (* (* (- (* i i) (* beta beta)) i) (- i beta)) (* (- i beta) (* alpha (- (* i i) (* beta beta))))))
592.0ms
(/ (+ (+ alpha beta) i) (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
589.0ms
(/ i (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
585.0ms
(/ (+ (+ alpha beta) i) (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
547.0ms
(sqrt (* (+ i alpha) (- (* beta beta) (* i i))))

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 37.1b

regimes307.0ms

Accuracy

49.7% (1.4b remaining)

Error of 37.9b against oracle of 36.5b and baseline of 39.2b

bsearch116.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.7s8000×body80valid
377.0ms8000×pre80true