Average Error: 3.5 → 1.1
Time: 3.7m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\alpha \le 3.0718281463403067 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{1}{\frac{2 + \left(\alpha + \beta\right)}{\frac{1.0 + \left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right)}{2 + \left(\alpha + \beta\right)}}}}{\left(2 + \left(\alpha + \beta\right)\right) + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{\beta}{\alpha} + \left(\frac{\alpha}{\beta} + 2\right)}}{\left(2 + \left(\alpha + \beta\right)\right) + 1.0}\\ \end{array}\]

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 +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: 3.7m)Debug log

sample82.0ms

Algorithm
intervals
Results
55.0ms256×body80valid
9.0ms256×pre80true

simplify774.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
774.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize57.0ms

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))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
531×times-frac
257×add-cube-cbrt
257×*-un-lft-identity
257×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×log1p-expm1-u
4×pow1
4×expm1-log1p-u
3×frac-2neg
3×fma-def
3×clear-num
1×sum-log
1×associate-+l+
1×+-commutative
Counts
4 → 360
Calls
4 calls:
Slowest
113.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
77.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
62.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
6.0ms
(+ (+ alpha beta) (* beta alpha))

series244.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
77.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
67.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
16.0ms
(+ (+ alpha beta) (* beta alpha))

simplify1.8m

Counts
526 → 372
Calls
526 calls:
Slowest
1.0s
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) 1)
987.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (pow (+ alpha beta) 3) (pow (* 2 1) 3))) 1)
931.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (pow (+ alpha beta) 3) (pow (* 2 1) 3))) 1) 1)
901.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
891.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (pow (+ alpha beta) 3) (pow (* 2 1) 3))) 1)

prune4.8s

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))))

rewrite115.0ms

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×log1p-expm1-u
4×frac-2neg
4×clear-num
4×expm1-log1p-u
1×inv-pow
1×pow-flip
Counts
4 → 226
Calls
4 calls:
Slowest
52.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
28.0ms
(/ (+ (+ 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))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
10.0ms
(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
97.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
78.0ms
(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))
65.0ms
(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))
44.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify44.7s

Counts
250 → 238
Calls
250 calls:
Slowest
820.0ms
(+ (pow (+ (+ alpha beta) (* beta alpha)) 3) (pow 1.0 3))
779.0ms
(- (* (+ (+ alpha beta) (* beta alpha)) (+ (+ alpha beta) (* beta alpha))) (* 1.0 1.0))
697.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
622.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
608.0ms
(/ (cbrt (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 2 beta) alpha))
3.4b
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 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))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
64×sqrt-div
50×*-un-lft-identity
48×flip-+
48×flip3-+
30×add-cube-cbrt
30×add-sqr-sqrt
24×frac-add
24×times-frac
24×frac-times
14×sqrt-prod
14×associate-*r*
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×associate-/l/
4×add-log-exp
4×log1p-expm1-u
4×associate-/r/
4×associate-*l/
4×pow-prod-down
4×pow1/2
4×expm1-log1p-u
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
23.0ms
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))
20.0ms
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))
13.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 2 beta) alpha))
13.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 2 beta) alpha))

series171.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
57.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 2 beta) alpha))
43.0ms
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))
40.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 2 beta) alpha))
31.0ms
(* (sqrt (+ (+ 2 beta) alpha)) (sqrt (+ (+ beta 1.0) (+ alpha 2))))

simplify21.6s

Counts
180 → 182
Calls
180 calls:
Slowest
767.0ms
(* (sqrt (- (+ 2 beta) alpha)) (sqrt (* (+ (* beta beta) (- (* 1.0 1.0) (* beta 1.0))) (+ (* alpha alpha) (- (* 2 2) (* alpha 2))))))
580.0ms
(* (sqrt (+ (pow (+ 2 beta) 3) (pow alpha 3))) (sqrt (+ (+ beta 1.0) (+ alpha 2))))
499.0ms
(sqrt (* (+ (* beta beta) (- (* 1.0 1.0) (* beta 1.0))) (- alpha 2)))
483.0ms
(sqrt (* (+ (* beta beta) (- (* 1.0 1.0) (* beta 1.0))) (- alpha 2)))
469.0ms
(* (sqrt (+ (pow (+ 2 beta) 3) (pow alpha 3))) (sqrt (+ (+ beta 1.0) (+ alpha 2))))

prune3.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 1.0 alpha) (+ 2 beta)))
3.0b
(/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 1.0 alpha) (+ 2 beta))) (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))))
0.0b
(* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha)))
0.0b
(+ (+ 1.0 alpha) (+ 2 beta))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
74×times-frac
35×add-cube-cbrt
35×add-sqr-sqrt
33×flip-+
33×flip3-+
30×associate-/l*
27×distribute-lft-out
26×associate-/r/
20×add-exp-log
20×add-cbrt-cube
16×frac-add
9×pow1
8×frac-times
7×div-exp
7×cbrt-undiv
6×add-log-exp
5×associate-/r*
4×div-inv
4×log1p-expm1-u
4×associate-*r/
4×associate-*l/
4×expm1-log1p-u
3×associate-/l/
3×cbrt-unprod
3×prod-exp
3×associate-*l*
3×associate-*r*
3×fma-def
2×frac-2neg
2×clear-num
1×pow-prod-up
1×*-commutative
1×pow-prod-down
1×pow-plus
1×distribute-lft-in
1×sum-log
1×associate-+r+
1×associate-+l+
1×+-commutative
1×distribute-rgt-in
1×pow2
Counts
4 → 183
Calls
4 calls:
Slowest
43.0ms
(/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 1.0 alpha) (+ 2 beta))) (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))))
32.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 1.0 alpha) (+ 2 beta)))
8.0ms
(* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha)))
7.0ms
(+ (+ 1.0 alpha) (+ 2 beta))

series163.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 1.0 alpha) (+ 2 beta))) (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))))
41.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ (+ 1.0 alpha) (+ 2 beta)))
13.0ms
(* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha)))
12.0ms
(+ (+ 1.0 alpha) (+ 2 beta))

simplify28.1s

Counts
192 → 195
Calls
192 calls:
Slowest
1.1s
(* (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))) (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
863.0ms
(* (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))) (+ (* 2 2) (- (* (+ beta alpha) (+ beta alpha)) (* 2 (+ beta alpha)))))
587.0ms
(* (+ (* 1.0 1.0) (- (* alpha alpha) (* 1.0 alpha))) (+ (* 2 2) (- (* beta beta) (* 2 beta))))
496.0ms
(* (+ (* 1.0 1.0) (- (* alpha alpha) (* 1.0 alpha))) (+ (* 2 2) (- (* beta beta) (* 2 beta))))
493.0ms
(/ (/ 1 (+ (+ 1.0 alpha) (+ 2 beta))) (+ 2 (+ beta alpha)))

prune2.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes140.0ms

Accuracy

70.6% (1.0b remaining)

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

bsearch152.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.4s8000×body80valid
690.0ms8000×pre80true