Average Error: 3.5 → 1.1
Time: 3.0m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\alpha \le 3.0718281463403067 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{1}{\frac{2 + \left(\alpha + \beta\right)}{\frac{1.0 + \left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right)}{2 + \left(\alpha + \beta\right)}}}}{\left(2 + \left(\alpha + \beta\right)\right) + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{\beta}{\alpha} + \left(\frac{\alpha}{\beta} + 2\right)}}{\left(2 + \left(\alpha + \beta\right)\right) + 1.0}\\ \end{array}\]

Error

Bits error versus alpha

Bits error versus beta

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if alpha < 3.0718281463403067e+159

    1. Initial program 1.2

      \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity1.2

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

    4. Applied *-un-lft-identity1.2

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

    5. Applied times-frac1.2

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

    6. Applied associate-/l*1.3

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

    7. Simplified1.3

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

    if 3.0718281463403067e+159 < alpha

    1. Initial program 15.4

      \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity15.4

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

    4. Applied *-un-lft-identity15.4

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

    5. Applied times-frac15.4

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

    6. Applied associate-/l*15.4

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

    7. Simplified15.4

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

    8. Taylor expanded around inf 0.1

      \[\leadsto \frac{\frac{1}{\color{blue}{\frac{\beta}{\alpha} + \left(2 + \frac{\alpha}{\beta}\right)}}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\alpha \le 3.0718281463403067 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{1}{\frac{2 + \left(\alpha + \beta\right)}{\frac{1.0 + \left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right)}{2 + \left(\alpha + \beta\right)}}}}{\left(2 + \left(\alpha + \beta\right)\right) + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{\beta}{\alpha} + \left(\frac{\alpha}{\beta} + 2\right)}}{\left(2 + \left(\alpha + \beta\right)\right) + 1.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2019022 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/3"
  :pre (and (> alpha -1) (> beta -1))
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))

Details

Time bar (total: 3.0m)Debug log

sample88.0ms

Algorithm
intervals
Results
58.0ms256×body80valid
10.0ms256×pre80true

simplify584.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
583.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize30.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.0b
(+ (+ alpha beta) (* beta alpha))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
531×times-frac
256×add-cube-cbrt
256×*-un-lft-identity
256×add-sqr-sqrt
69×associate-/l*
46×associate-/r/
25×flip-+
25×flip3-+
23×div-inv
20×add-exp-log
20×add-cbrt-cube
10×div-exp
10×cbrt-undiv
9×associate-/r*
6×add-log-exp
4×associate-/l/
4×pow1
3×frac-2neg
3×clear-num
1×sum-log
1×associate-+l+
1×+-commutative
Counts
4 → 349
Calls
4 calls:
Slowest
80.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
52.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
51.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
6.0ms
(+ (+ alpha beta) (* beta alpha))

series255.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
102.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
83.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
53.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
16.0ms
(+ (+ alpha beta) (* beta alpha))

simplify1.4m

Counts
524 → 361
Calls
524 calls:
Slowest
939.0ms
(/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
753.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
741.0ms
(/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
647.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (* (cbrt (+ (+ alpha beta) (* 2 1))) (cbrt (+ (+ alpha beta) (* 2 1))))) (* (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
643.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune4.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.1b

localize8.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
0.1b
(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))
0.0b
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
177×times-frac
103×add-cube-cbrt
103×*-un-lft-identity
103×add-sqr-sqrt
71×associate-/r*
28×add-exp-log
25×associate-/r/
16×div-inv
14×div-exp
13×add-cbrt-cube
11×associate-/l*
11×flip-+
11×flip3-+
6×rec-exp
5×associate-/l/
5×cbrt-undiv
5×pow1
4×add-log-exp
4×frac-2neg
4×clear-num
1×inv-pow
1×pow-flip
Counts
4 → 218
Calls
4 calls:
Slowest
57.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
34.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
24.0ms
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))
17.0ms
(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))
95.0ms
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))
82.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
52.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify31.3s

Counts
250 → 230
Calls
250 calls:
Slowest
762.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
727.0ms
(+ (pow (+ (+ alpha beta) (* beta alpha)) 3) (pow 1.0 3))
657.0ms
(- (* (+ (+ alpha beta) (* beta alpha)) (+ (+ alpha beta) (* beta alpha))) (* 1.0 1.0))
470.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
435.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize100.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ (+ 2 beta) alpha))
3.4b
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))
2.8b
(/ (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))) (* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2))))
0.5b
(* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
50×flip-+
50×flip3-+
41×*-un-lft-identity
39×add-cube-cbrt
39×add-sqr-sqrt
33×sqrt-prod
29×sqrt-div
28×associate-/r/
24×associate-/l*
24×frac-add
24×frac-times
15×add-exp-log
15×add-cbrt-cube
12×associate-*r/
7×associate-/r*
6×associate-*l*
6×pow1
5×associate-/l/
5×div-inv
4×add-log-exp
4×associate-*l/
4×associate-*r*
4×div-exp
4×cbrt-undiv
3×frac-2neg
3×clear-num
2×cbrt-unprod
2×prod-exp
1×distribute-lft-out
1×*-commutative
1×pow-prod-down
1×distribute-lft-in
1×distribute-rgt-in
Counts
4 → 177
Calls
4 calls:
Slowest
37.0ms
(/ (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))) (* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2))))
36.0ms
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ (+ 2 beta) alpha))
28.0ms
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))
8.0ms
(* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
66.0ms
(/ (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))) (* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2))))
58.0ms
(* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2)))
56.0ms
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ (+ 2 beta) alpha))
53.0ms
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))

simplify24.6s

Counts
195 → 189
Calls
195 calls:
Slowest
770.0ms
(+ (pow (+ (+ beta 1.0) (* alpha beta)) 3) (pow alpha 3))
704.0ms
(- (* (+ (+ beta 1.0) (* alpha beta)) (+ (+ beta 1.0) (* alpha beta))) (* alpha alpha))
659.0ms
(+ (pow (+ (+ beta 1.0) (* alpha beta)) 3) (pow alpha 3))
617.0ms
(- (* (+ (+ beta 1.0) (* alpha beta)) (+ (+ beta 1.0) (* alpha beta))) (* alpha alpha))
540.0ms
(/ (* (* (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))) (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha))))) (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha))))) (* (* (* (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (* (* (+ (+ beta alpha) (+ 1.0 2)) (+ (+ beta alpha) (+ 1.0 2))) (+ (+ beta alpha) (+ 1.0 2)))))

prune4.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ (+ beta 1.0) (+ alpha (* alpha beta))) (+ (+ 2 beta) alpha))
3.4b
(/ (+ (+ beta 1.0) (+ alpha (* alpha beta))) (+ (+ 2 beta) alpha))
0.7b
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))
0.7b
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
64×sqrt-div
56×flip-+
56×flip3-+
50×*-un-lft-identity
32×frac-add
30×add-cube-cbrt
30×add-sqr-sqrt
24×times-frac
24×frac-times
14×sqrt-prod
14×associate-*r*
12×associate-/l/
12×add-exp-log
12×associate-*r/
12×associate-*l*
12×add-cbrt-cube
10×distribute-lft-out
8×associate-/l*
8×pow1
6×associate-/r*
4×add-log-exp
4×associate-/r/
4×associate-*l/
4×pow-prod-down
4×pow1/2
2×div-inv
2×cbrt-unprod
2×*-commutative
2×prod-exp
2×div-exp
2×sqrt-unprod
2×frac-2neg
2×clear-num
2×cbrt-undiv
Counts
4 → 170
Calls
4 calls:
Slowest
25.0ms
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))
22.0ms
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))
21.0ms
(/ (+ (+ beta 1.0) (+ alpha (* alpha beta))) (+ (+ 2 beta) alpha))
16.0ms
(/ (+ (+ beta 1.0) (+ alpha (* alpha beta))) (+ (+ 2 beta) alpha))

series182.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
49.0ms
(/ (+ (+ beta 1.0) (+ alpha (* alpha beta))) (+ (+ 2 beta) alpha))
48.0ms
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))
46.0ms
(/ (+ (+ beta 1.0) (+ alpha (* alpha beta))) (+ (+ 2 beta) alpha))
38.0ms
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))

simplify19.7s

Counts
188 → 182
Calls
188 calls:
Slowest
523.0ms
(- (+ (* 2.0 (/ 1 (pow beta 2))) 1) (* 1.0 (/ 1 beta)))
397.0ms
(* (sqrt (- (+ 2 beta) alpha)) (sqrt (* (+ (* beta beta) (- (* 1.0 1.0) (* beta 1.0))) (+ (* alpha alpha) (- (* 2 2) (* alpha 2))))))
396.0ms
(sqrt (* (+ (* beta beta) (- (* 1.0 1.0) (* beta 1.0))) (+ (* alpha alpha) (- (* 2 2) (* alpha 2)))))
388.0ms
(* (sqrt (- (+ 2 beta) alpha)) (sqrt (* (+ (* beta beta) (- (* 1.0 1.0) (* beta 1.0))) (+ (* alpha alpha) (- (* 2 2) (* alpha 2))))))
356.0ms
(* (sqrt (+ (pow (+ 2 beta) 3) (pow alpha 3))) (sqrt (- (* (+ beta 1.0) (+ beta 1.0)) (* (+ alpha 2) (+ alpha 2)))))

prune3.7s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes196.0ms

Accuracy

70.6% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.5b

bsearch128.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.3s8000×body80valid
249.0ms8000×pre80true