Average Error: 23.2 → 12.1
Time: 38.0s
Precision: 64
Internal Precision: 128
\[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
↓
\[\frac{\sqrt[3]{(\left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\beta - \alpha\right)\right)\right) \cdot \left(\frac{\alpha + \beta}{\beta + (2 \cdot i + \alpha)_*}\right) + 1.0)_* \cdot \left((\left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\beta - \alpha\right)\right)\right) \cdot \left(\frac{\alpha + \beta}{\beta + (2 \cdot i + \alpha)_*}\right) + 1.0)_* \cdot (\left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\beta - \alpha\right)\right)\right) \cdot \left(\frac{\alpha + \beta}{\beta + (2 \cdot i + \alpha)_*}\right) + 1.0)_*\right)}}{2.0}\]

Error

Bits error versus alpha

Bits error versus beta

Bits error versus i

Derivation

  1. Initial program 23.2

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

  2. Simplified12.0

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

  4. Applied div-inv12.0

    \[\leadsto \frac{(\color{blue}{\left(\left(\beta - \alpha\right) \cdot \frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}\right)} \cdot \left(\frac{\beta + \alpha}{(2 \cdot i + \alpha)_* + \beta}\right) + 1.0)_*}{2.0}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt12.1

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

  7. Applied associate-*r*12.1

    \[\leadsto \frac{(\color{blue}{\left(\left(\left(\beta - \alpha\right) \cdot \sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}}\right) \cdot \sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}}\right)} \cdot \left(\frac{\beta + \alpha}{(2 \cdot i + \alpha)_* + \beta}\right) + 1.0)_*}{2.0}\]
  8. Using strategy rm

  9. Applied add-cbrt-cube12.1

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left((\left(\left(\left(\beta - \alpha\right) \cdot \sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}}\right) \cdot \sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}}\right) \cdot \left(\frac{\beta + \alpha}{(2 \cdot i + \alpha)_* + \beta}\right) + 1.0)_* \cdot (\left(\left(\left(\beta - \alpha\right) \cdot \sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}}\right) \cdot \sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}}\right) \cdot \left(\frac{\beta + \alpha}{(2 \cdot i + \alpha)_* + \beta}\right) + 1.0)_*\right) \cdot (\left(\left(\left(\beta - \alpha\right) \cdot \sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}}\right) \cdot \sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}}\right) \cdot \left(\frac{\beta + \alpha}{(2 \cdot i + \alpha)_* + \beta}\right) + 1.0)_*}}}{2.0}\]

  10. Final simplification12.1

    \[\leadsto \frac{\sqrt[3]{(\left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\beta - \alpha\right)\right)\right) \cdot \left(\frac{\alpha + \beta}{\beta + (2 \cdot i + \alpha)_*}\right) + 1.0)_* \cdot \left((\left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\beta - \alpha\right)\right)\right) \cdot \left(\frac{\alpha + \beta}{\beta + (2 \cdot i + \alpha)_*}\right) + 1.0)_* \cdot (\left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\sqrt{\frac{1}{\left(\beta + 2.0\right) + (2 \cdot i + \alpha)_*}} \cdot \left(\beta - \alpha\right)\right)\right) \cdot \left(\frac{\alpha + \beta}{\beta + (2 \cdot i + \alpha)_*}\right) + 1.0)_*\right)}}{2.0}\]

Reproduce

herbie shell --seed 2019010 +o rules:numerics
(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: 36.2s)Debug log

sample67.0ms

Algorithm
intervals

simplify634.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
634.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize50.0ms

Local error

Found 3 expressions with local error:

1.7b
(fma (/ (- beta alpha) (+ (+ beta 2.0) (fma 2 i alpha))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
0.0b
(/ (+ beta alpha) (+ (fma 2 i alpha) beta))
0.0b
(/ (- beta alpha) (+ (+ beta 2.0) (fma 2 i alpha)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
21×times-frac
20×add-cube-cbrt
20×add-sqr-sqrt
7×add-exp-log
7×add-cbrt-cube
7×associate-/r*
6×associate-/l*
4×associate-/l/
4×distribute-lft-out
4×associate-/r/
3×add-log-exp
3×log1p-expm1-u
3×flip-+
3×flip3-+
3×pow1
3×expm1-log1p-u
2×div-inv
2×div-exp
2×frac-2neg
2×clear-num
2×cbrt-undiv
1×flip--
1×fma-udef
1×div-sub
1×flip3--
Counts
3 → 81
Calls
3 calls:
Slowest
12.0ms
(/ (- beta alpha) (+ (+ beta 2.0) (fma 2 i alpha)))
11.0ms
(/ (+ beta alpha) (+ (fma 2 i alpha) beta))
0.0ms
(fma (/ (- beta alpha) (+ (+ beta 2.0) (fma 2 i alpha))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)

series243.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
136.0ms
(fma (/ (- beta alpha) (+ (+ beta 2.0) (fma 2 i alpha))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
67.0ms
(/ (- beta alpha) (+ (+ beta 2.0) (fma 2 i alpha)))
39.0ms
(/ (+ beta alpha) (+ (fma 2 i alpha) beta))

simplify3.1s

Counts
75 → 90
Calls
75 calls:
Slowest
353.0ms
(+ (* (+ beta 2.0) (+ beta 2.0)) (- (* (fma 2 i alpha) (fma 2 i alpha)) (* (+ beta 2.0) (fma 2 i alpha))))
189.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
179.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
160.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ beta 2.0) (fma 2 i alpha)) (+ (+ beta 2.0) (fma 2 i alpha))) (+ (+ beta 2.0) (fma 2 i alpha))))
144.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b
(fma (* (- beta alpha) (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
0.2b
(* (- beta alpha) (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))
0.0b
(/ (+ beta alpha) (+ (fma 2 i alpha) beta))
0.0b
(/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
15×add-cube-cbrt
15×add-sqr-sqrt
11×add-exp-log
9×times-frac
8×add-cbrt-cube
7×associate-/r*
7×pow1
6×associate-/r/
6×associate-*r*
4×add-log-exp
4×log1p-expm1-u
4×flip-+
4×flip3-+
4×expm1-log1p-u
3×associate-/l*
3×div-inv
3×associate-*l*
2×associate-/l/
2×flip--
2×prod-exp
2×associate-*l/
2×flip3--
2×frac-2neg
2×clear-num
2×rec-exp
2×frac-times
1×inv-pow
1×distribute-lft-out
1×pow-flip
1×fma-udef
1×cbrt-unprod
1×*-commutative
1×un-div-inv
1×associate-*r/
1×pow-prod-down
1×div-exp
1×cbrt-undiv
Counts
4 → 93
Calls
4 calls:
Slowest
5.0ms
(/ (+ beta alpha) (+ (fma 2 i alpha) beta))
5.0ms
(* (- beta alpha) (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))
3.0ms
(/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))
0.0ms
(fma (* (- beta alpha) (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)

series320.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(fma (* (- beta alpha) (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
77.0ms
(* (- beta alpha) (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))
65.0ms
(/ (+ beta alpha) (+ (fma 2 i alpha) beta))
52.0ms
(/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))

simplify4.4s

Counts
68 → 105
Calls
68 calls:
Slowest
436.0ms
(+ (* (+ beta 2.0) (+ beta 2.0)) (- (* (fma 2 i alpha) (fma 2 i alpha)) (* (+ beta 2.0) (fma 2 i alpha))))
428.0ms
(* (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))) (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))) (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))
362.0ms
(* (+ beta alpha) (+ (+ beta 2.0) (fma 2 i alpha)))
357.0ms
(+ (* (+ beta 2.0) (+ beta 2.0)) (- (* (fma 2 i alpha) (fma 2 i alpha)) (* (+ beta 2.0) (fma 2 i alpha))))
241.0ms
(* (- (pow beta 3) (pow alpha 3)) (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.1b

localize14.0ms

Local error

Found 4 expressions with local error:

7.2b
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
0.3b
(* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))
0.3b
(* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))
0.1b
(sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
18×associate-*r*
16×sqrt-div
11×add-exp-log
11×associate-*l/
11×add-cbrt-cube
11×pow1
11×frac-times
11×add-sqr-sqrt
10×add-cube-cbrt
10×*-un-lft-identity
6×flip--
6×associate-/r/
6×flip3--
4×add-log-exp
4×log1p-expm1-u
4×cbrt-unprod
4×associate-*r/
4×prod-exp
4×pow-prod-down
4×associate-*l*
4×expm1-log1p-u
3×div-inv
3×flip-+
3×flip3-+
2×*-commutative
1×fma-udef
1×pow1/2
1×rem-sqrt-square
Counts
4 → 95
Calls
4 calls:
Slowest
14.0ms
(* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))
11.0ms
(* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))
3.0ms
(sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))
0.0ms
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)

series365.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))
95.0ms
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
79.0ms
(sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))
65.0ms
(* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))

simplify9.8s

Counts
73 → 107
Calls
73 calls:
Slowest
867.0ms
(* (* (- (* beta beta) (* alpha alpha)) (sqrt 1)) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))
625.0ms
(* (* (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))) (* (* (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))))
549.0ms
(* (* (+ beta alpha) (sqrt (+ (+ beta 2.0) (fma 2 i alpha)))) (sqrt (+ (+ beta 2.0) (fma 2 i alpha))))
470.0ms
(sqrt (+ (* (+ beta 2.0) (+ beta 2.0)) (- (* (fma 2 i alpha) (fma 2 i alpha)) (* (+ beta 2.0) (fma 2 i alpha)))))
423.0ms
(sqrt (+ (* (+ beta 2.0) (+ beta 2.0)) (- (* (fma 2 i alpha) (fma 2 i alpha)) (* (+ beta 2.0) (fma 2 i alpha)))))

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

localize23.0ms

Local error

Found 4 expressions with local error:

7.2b
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
7.2b
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
7.2b
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
0.3b
(* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-div
9×add-exp-log
9×associate-*l/
9×associate-*r*
9×add-cbrt-cube
9×pow1
9×frac-times
6×sqrt-prod
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
4×add-log-exp
4×flip--
4×log1p-expm1-u
4×flip3--
4×expm1-log1p-u
3×fma-udef
3×cbrt-unprod
3×associate-*r/
3×prod-exp
3×pow-prod-down
2×associate-/r/
1×div-inv
1×flip-+
1×*-commutative
1×associate-*l*
1×flip3-+
Counts
4 → 67
Calls
4 calls:
Slowest
13.0ms
(* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))
0.0ms
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
0.0ms
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
0.0ms
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)

series466.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
136.0ms
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
122.0ms
(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (/ (+ beta alpha) (+ (fma 2 i alpha) beta)) 1.0)
51.0ms
(* (* (- beta alpha) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))

simplify6.7s

Counts
44 → 79
Calls
44 calls:
Slowest
667.0ms
(* (* (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))) (* (* (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))))
517.0ms
(* (* (+ beta alpha) (sqrt (+ (+ beta 2.0) (fma 2 i alpha)))) (sqrt (+ (+ beta 2.0) (fma 2 i alpha))))
405.0ms
(sqrt (+ (* (+ beta 2.0) (+ beta 2.0)) (- (* (fma 2 i alpha) (fma 2 i alpha)) (* (+ beta 2.0) (fma 2 i alpha)))))
391.0ms
(* (* (- (* beta beta) (* alpha alpha)) (sqrt 1)) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha)))))
372.0ms
(* (* (- (* beta beta) (* alpha alpha)) (sqrt (/ 1 (+ (+ beta 2.0) (fma 2 i alpha))))) (sqrt 1))

prune1.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.1b

regimes863.0ms

Accuracy

0% (0.3b remaining)

Error of 12.1b against oracle of 11.8b and baseline of 12.1b

bsearch3.0ms

end0.0ms

sample3.2s

Algorithm
intervals