Average Error: 3.6 → 2.5
Time: 9.7m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\beta \le 6.377535961616027 \cdot 10^{+161}:\\ \;\;\;\;\frac{\frac{1}{\left(\beta + 2\right) + \left(1.0 + \alpha\right)}}{\left(\beta + \alpha\right) + 2} \cdot \frac{\left(1.0 + \alpha\right) + (\beta \cdot \alpha + \beta)_*}{\left(\beta + \alpha\right) + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\left(\beta + 2\right) + \left(1.0 + \alpha\right)}}{\left(\beta + \alpha\right) + 2} \cdot (\left(\beta + \alpha\right) \cdot 0.25 + 0.5)_*\\ \end{array}\]

Error

Bits error versus alpha

Bits error versus beta

Derivation

  1. Split input into 2 regimes

  2. if beta < 6.377535961616027e+161

    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

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

    4. Applied div-inv1.2

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

    5. Applied times-frac1.5

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

    6. Simplified1.5

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

    7. Simplified1.5

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

    if 6.377535961616027e+161 < beta

    1. Initial program 15.8

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

    3. Applied *-un-lft-identity15.8

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

    4. Applied div-inv15.8

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

    5. Applied times-frac17.1

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

    6. Simplified17.1

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

    7. Simplified17.1

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

    8. Taylor expanded around 0 7.6

      \[\leadsto \color{blue}{\left(0.25 \cdot \alpha + \left(0.25 \cdot \beta + 0.5\right)\right)} \cdot \frac{\frac{1}{\left(\beta + 2\right) + \left(\alpha + 1.0\right)}}{\left(\alpha + \beta\right) + 2}\]

    9. Simplified7.6

      \[\leadsto \color{blue}{(\left(\alpha + \beta\right) \cdot 0.25 + 0.5)_*} \cdot \frac{\frac{1}{\left(\beta + 2\right) + \left(\alpha + 1.0\right)}}{\left(\alpha + \beta\right) + 2}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\beta \le 6.377535961616027 \cdot 10^{+161}:\\ \;\;\;\;\frac{\frac{1}{\left(\beta + 2\right) + \left(1.0 + \alpha\right)}}{\left(\beta + \alpha\right) + 2} \cdot \frac{\left(1.0 + \alpha\right) + (\beta \cdot \alpha + \beta)_*}{\left(\beta + \alpha\right) + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\left(\beta + 2\right) + \left(1.0 + \alpha\right)}}{\left(\beta + \alpha\right) + 2} \cdot (\left(\beta + \alpha\right) \cdot 0.25 + 0.5)_*\\ \end{array}\]

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(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: 9.6m)Debug log

sample44.0ms

Algorithm
intervals
Results
256×(pre true 80)
256×(body real 80)

simplify726.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
726.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.3b

localize38.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ (+ (+ 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) (* 2 1)) 1.0)
0.0b
(+ (+ alpha beta) (* beta alpha))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
450×times-frac
214×add-cube-cbrt
214×*-un-lft-identity
214×add-sqr-sqrt
54×associate-/l*
36×associate-/r/
21×flip-+
21×flip3-+
18×div-inv
15×add-exp-log
15×add-cbrt-cube
7×div-exp
7×cbrt-undiv
6×add-log-exp
6×fma-def
6×associate-/r*
4×log1p-expm1-u
4×pow1
4×expm1-log1p-u
3×associate-/l/
2×frac-2neg
2×clear-num
2×associate-+l+
2×+-commutative
1×sum-log
Counts
4 → 294
Calls
4 calls:
Slowest
88.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
36.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
13.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
4.0ms
(+ (+ alpha beta) (* beta alpha))

series180.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
95.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
63.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
13.0ms
(+ (+ alpha beta) (* beta alpha))
8.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)

simplify1.6m

Counts
415 → 306
Calls
415 calls:
Slowest
1.1s
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) 1)
1.1s
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (pow (+ alpha beta) 3) (pow (* 2 1) 3))) 1)
1.0s
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
842.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (pow (+ alpha beta) 3) (pow (* 2 1) 3))) 1) 1)
820.0ms
(/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune4.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ (+ 1.0 alpha) (fma beta alpha beta)) (+ 2 (+ beta alpha)))
0.3b
(* (/ (+ (+ 1.0 alpha) (fma beta alpha beta)) (+ 2 (+ beta alpha))) (/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2)))
0.1b
(/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2))
0.0b
(/ 1 (+ (+ beta 2) (+ alpha 1.0)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
67×*-un-lft-identity
56×associate-/r/
51×add-cube-cbrt
51×add-sqr-sqrt
45×flip-+
45×flip3-+
36×associate-*r*
32×frac-add
30×add-exp-log
20×add-cbrt-cube
18×associate-*l*
14×associate-/l*
12×div-inv
10×div-exp
10×associate-/r*
8×distribute-lft-out
7×pow1
6×prod-exp
6×cbrt-undiv
4×add-log-exp
4×log1p-expm1-u
4×cbrt-unprod
4×rec-exp
4×expm1-log1p-u
3×associate-/l/
3×frac-2neg
3×clear-num
1×inv-pow
1×pow-flip
1×*-commutative
1×associate-*r/
1×associate-*l/
1×pow-prod-down
1×frac-times
Counts
4 → 201
Calls
4 calls:
Slowest
20.0ms
(/ (+ (+ 1.0 alpha) (fma beta alpha beta)) (+ 2 (+ beta alpha)))
16.0ms
(* (/ (+ (+ 1.0 alpha) (fma beta alpha beta)) (+ 2 (+ beta alpha))) (/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2)))
11.0ms
(/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2))
3.0ms
(/ 1 (+ (+ beta 2) (+ alpha 1.0)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(* (/ (+ (+ 1.0 alpha) (fma beta alpha beta)) (+ 2 (+ beta alpha))) (/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2)))
56.0ms
(/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2))
46.0ms
(/ (+ (+ 1.0 alpha) (fma beta alpha beta)) (+ 2 (+ beta alpha)))
31.0ms
(/ 1 (+ (+ beta 2) (+ alpha 1.0)))

simplify32.2s

Counts
202 → 213
Calls
202 calls:
Slowest
1.0s
(+ (log (/ (+ (+ 1.0 alpha) (fma beta alpha beta)) (+ 2 (+ beta alpha)))) (log (/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2))))
991.0ms
(/ (/ 1 (- (* (+ beta 2) (+ beta 2)) (* (+ alpha 1.0) (+ alpha 1.0)))) 1)
708.0ms
(/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2))
633.0ms
(/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2))
602.0ms
(/ (/ 1 (+ (+ beta 2) (+ alpha 1.0))) (+ (+ alpha beta) 2))

prune3.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize91.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2)))
2.2b
(/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha))
0.1b
(/ (sqrt (/ (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha)) (+ (+ 2 beta) alpha))) (+ (+ 1.0 alpha) (+ 2 beta)))
0.1b
(sqrt (/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2))) (+ beta (+ alpha 2))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
819×times-frac
601×*-un-lft-identity
360×sqrt-prod
355×add-sqr-sqrt
349×add-cube-cbrt
126×distribute-lft-out
71×associate-/l*
58×associate-/r/
33×flip-+
33×flip3-+
27×div-inv
10×add-exp-log
10×add-cbrt-cube
10×associate-/r*
5×associate-/l/
4×add-log-exp
4×log1p-expm1-u
4×frac-add
4×pow1
4×expm1-log1p-u
3×div-exp
3×frac-2neg
3×clear-num
3×rem-sqrt-square
3×cbrt-undiv
2×sqrt-div
1×pow1/2
Counts
4 → 488
Calls
4 calls:
Slowest
48.0ms
(/ (sqrt (/ (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha)) (+ (+ 2 beta) alpha))) (+ (+ 1.0 alpha) (+ 2 beta)))
22.0ms
(/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha))
16.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2)))
13.0ms
(sqrt (/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2))) (+ beta (+ alpha 2))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(sqrt (/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2))) (+ beta (+ alpha 2))))
74.0ms
(/ (sqrt (/ (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha)) (+ (+ 2 beta) alpha))) (+ (+ 1.0 alpha) (+ 2 beta)))
49.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2)))
44.0ms
(/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha))

simplify1.7m

Counts
725 → 500
Calls
725 calls:
Slowest
941.0ms
(sqrt (/ (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha)) (- (* (+ 2 beta) (+ 2 beta)) (* alpha alpha))))
551.0ms
(/ (sqrt (/ (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha)) (- (* (+ 2 beta) (+ 2 beta)) (* alpha alpha)))) (* (cbrt (+ (+ 1.0 alpha) (+ 2 beta))) (cbrt (+ (+ 1.0 alpha) (+ 2 beta)))))
543.0ms
(/ (sqrt (/ (+ (* (+ 2 beta) (+ 2 beta)) (- (* alpha alpha) (* (+ 2 beta) alpha))) (cbrt (+ (+ 2 beta) alpha)))) (sqrt (+ (+ 1.0 alpha) (+ 2 beta))))
526.0ms
(/ (sqrt (/ (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha)) (- (* (+ 2 beta) (+ 2 beta)) (* alpha alpha)))) 1)
523.0ms
(/ (sqrt (/ (/ (cbrt (+ (+ beta 1.0) (fma beta alpha alpha))) (cbrt (+ (+ 2 beta) alpha))) (+ (+ 2 beta) alpha))) (cbrt (+ (+ 1.0 alpha) (+ 2 beta))))

prune10.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha)))
0.7b
(/ (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha))) (fma (+ beta alpha) (+ beta alpha) -4))
0.0b
(/ (/ (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha))) (fma (+ beta alpha) (+ beta alpha) -4)) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1))))
0.0b
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
2964×times-frac
1493×*-un-lft-identity
1173×add-cube-cbrt
1173×add-sqr-sqrt
227×associate-/r/
160×distribute-lft-out
131×div-inv
83×associate-/l*
60×flip--
60×flip3--
55×flip-+
55×flip3-+
34×add-exp-log
34×add-cbrt-cube
24×associate-/r*
20×div-exp
20×cbrt-undiv
6×associate-/l/
4×add-log-exp
4×log1p-expm1-u
4×frac-2neg
4×clear-num
4×pow1
4×expm1-log1p-u
Counts
4 → 1131
Calls
4 calls:
Slowest
51.0ms
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
48.0ms
(/ (/ (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha))) (fma (+ beta alpha) (+ beta alpha) -4)) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1))))
17.0ms
(/ (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha))) (fma (+ beta alpha) (+ beta alpha) -4))
12.0ms
(/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(/ (/ (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha))) (fma (+ beta alpha) (+ beta alpha) -4)) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1))))
115.0ms
(/ (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha))) (fma (+ beta alpha) (+ beta alpha) -4))
43.0ms
(/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha)))
34.0ms
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))

simplify5.2m

Counts
2035 → 1143
Calls
2035 calls:
Slowest
869.0ms
(/ (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ (pow 2 3) (pow (+ beta alpha) 3))) 1)
745.0ms
(/ (/ (* (* (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha))) (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha)))) (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ 2 (+ beta alpha)))) (* (* (fma (+ beta alpha) (+ beta alpha) -4) (fma (+ beta alpha) (+ beta alpha) -4)) (fma (+ beta alpha) (+ beta alpha) -4))) (/ (* (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (* (* (- (+ alpha beta) (* 2 1)) (- (+ alpha beta) (* 2 1))) (- (+ alpha beta) (* 2 1)))))
598.0ms
(/ (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ (pow 2 3) (pow (+ beta alpha) 3))) 1)
592.0ms
(/ (/ (/ (+ (fma alpha beta 1.0) (+ beta alpha)) (+ (pow 2 3) (pow (+ beta alpha) 3))) 1) 1)
579.0ms
(/ (/ (/ (* (cbrt (+ (fma alpha beta 1.0) (+ beta alpha))) (cbrt (+ (fma alpha beta 1.0) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (* (cbrt (fma (+ beta alpha) (+ beta alpha) -4)) (cbrt (fma (+ beta alpha) (+ beta alpha) -4)))) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (pow (+ alpha beta) 3) (pow (* 2 1) 3))))

prune15.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes111.0ms

Accuracy

54.4% (1.3b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 4.1b

bsearch86.0ms

end0.0ms

sample1.1s

Algorithm
intervals
Results
8000×(pre true 80)
8000×(body real 80)