Average Error: 3.5 → 2.3
Time: 5.9m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\beta \le 1.2527931344298723 \cdot 10^{+186}:\\ \;\;\;\;\frac{\frac{\frac{\left(1.0 + \beta\right) + (\alpha \cdot \beta + \alpha)_*}{\beta + \left(\alpha + 2\right)}}{\left(\alpha + \beta\right) + 2}}{\left(\left(\alpha + \beta\right) + 2\right) + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{\left(1.0 + \beta\right) + \alpha}{\beta + \left(\alpha + 2\right)}}{\left(\alpha + \beta\right) + 2}}{\left(\left(\alpha + \beta\right) + 2\right) + 1.0}\\ \end{array}\]

Error

Bits error versus alpha

Bits error versus beta

Derivation

  1. Split input into 2 regimes

  2. if beta < 1.2527931344298723e+186

    1. Initial program 1.7

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

    3. Applied *-un-lft-identity1.7

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

    4. Applied add-sqr-sqrt1.8

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

    5. Applied times-frac1.8

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

    6. Simplified1.8

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

    7. Simplified1.8

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

    9. Applied pow11.8

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

    10. Applied pow11.8

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

    11. Applied pow-prod-down1.8

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

    12. Simplified1.7

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

    if 1.2527931344298723e+186 < beta

    1. Initial program 15.2

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

    3. Applied *-un-lft-identity15.2

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

    4. Applied add-sqr-sqrt15.2

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

    5. Applied times-frac15.2

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

    6. Simplified15.2

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

    7. Simplified15.2

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

    9. Applied pow115.2

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

    10. Applied pow115.2

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

    11. Applied pow-prod-down15.2

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

    12. Simplified15.2

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

    13. Taylor expanded around 0 5.8

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\beta \le 1.2527931344298723 \cdot 10^{+186}:\\ \;\;\;\;\frac{\frac{\frac{\left(1.0 + \beta\right) + (\alpha \cdot \beta + \alpha)_*}{\beta + \left(\alpha + 2\right)}}{\left(\alpha + \beta\right) + 2}}{\left(\left(\alpha + \beta\right) + 2\right) + 1.0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{\left(1.0 + \beta\right) + \alpha}{\beta + \left(\alpha + 2\right)}}{\left(\alpha + \beta\right) + 2}}{\left(\left(\alpha + \beta\right) + 2\right) + 1.0}\\ \end{array}\]

Reproduce

herbie shell --seed 2018365 +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: 5.8m)Debug log

start92.0ms

Algorithm
intervals

setup831.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.8b

localize34.0ms

Local error

Found 4 expressions with local error:

1.7b
(/ (+ (+ (+ 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))

rewrite255.0ms

Algorithm
rewrite-expression-head
Counts
4 → 360
Calls

4 calls. Slowest were:

111.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
79.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
49.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series298.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

123.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
107.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
52.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
16.0ms
(+ (+ alpha beta) (* beta alpha))

simplify2.1m

Counts
526 → 372
Calls

526 calls. Slowest were:

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)
1.0s
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (pow (+ alpha beta) 3) (pow (* 2 1) 3))) 1)

prune7.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

1.7b
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2)))
1.7b
(/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha))
0.1b
(* (sqrt (/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2))) (+ beta (+ alpha 2)))) (/ (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))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Counts
4 → 491
Calls

4 calls. Slowest were:

32.0ms
(* (sqrt (/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2))) (+ beta (+ alpha 2)))) (/ (sqrt (/ (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha)) (+ (+ 2 beta) alpha))) (+ (+ 1.0 alpha) (+ 2 beta))))
29.0ms
(/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha))
13.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2)))

series480.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

258.0ms
(* (sqrt (/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2))) (+ beta (+ alpha 2)))) (/ (sqrt (/ (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha)) (+ (+ 2 beta) alpha))) (+ (+ 1.0 alpha) (+ 2 beta))))
126.0ms
(sqrt (/ (/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2))) (+ beta (+ alpha 2))))
50.0ms
(/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha))
46.0ms
(/ (+ (fma beta alpha beta) (+ 1.0 alpha)) (+ beta (+ alpha 2)))

simplify1.2m

Counts
479 → 503
Calls

479 calls. Slowest were:

598.0ms
(/ (sqrt (/ (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha)) (+ (+ 2 beta) alpha))) (+ (+ 1.0 alpha) (+ 2 beta)))
518.0ms
(* (+ (* 1.0 1.0) (- (* alpha alpha) (* 1.0 alpha))) (+ (* 2 2) (- (* beta beta) (* 2 beta))))
497.0ms
(/ (sqrt (/ (sqrt (/ (+ (+ beta 1.0) (fma beta alpha alpha)) (+ (+ 2 beta) alpha))) (sqrt (+ (+ 2 beta) alpha)))) (sqrt (+ (+ 1.0 alpha) (+ 2 beta))))

prune12.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.7b
(sqrt (+ (fma beta alpha beta) (+ 1.0 alpha)))
1.7b
(sqrt (+ (fma alpha beta beta) (+ 1.0 alpha)))
0.2b
(* (sqrt (+ (fma beta alpha beta) (+ 1.0 alpha))) (/ (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha))) (+ (+ alpha 2) beta)))
0.1b
(/ (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha))) (+ (+ alpha 2) beta))

rewrite74.0ms

Algorithm
rewrite-expression-head
Counts
4 → 139
Calls

4 calls. Slowest were:

32.0ms
(* (sqrt (+ (fma beta alpha beta) (+ 1.0 alpha))) (/ (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha))) (+ (+ alpha 2) beta)))
22.0ms
(/ (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha))) (+ (+ alpha 2) beta))
8.0ms
(sqrt (+ (fma beta alpha beta) (+ 1.0 alpha)))

series393.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

156.0ms
(* (sqrt (+ (fma beta alpha beta) (+ 1.0 alpha))) (/ (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha))) (+ (+ alpha 2) beta)))
145.0ms
(/ (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha))) (+ (+ alpha 2) beta))
49.0ms
(sqrt (+ (fma beta alpha beta) (+ 1.0 alpha)))
42.0ms
(sqrt (+ (fma alpha beta beta) (+ 1.0 alpha)))

simplify14.2s

Counts
130 → 151
Calls

130 calls. Slowest were:

663.0ms
(sqrt (- (* (fma beta alpha beta) (fma beta alpha beta)) (* (+ 1.0 alpha) (+ 1.0 alpha))))
307.0ms
(* (sqrt (- (* (fma beta alpha beta) (fma beta alpha beta)) (* (+ 1.0 alpha) (+ 1.0 alpha)))) (/ (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha))) (+ (+ alpha 2) beta)))
304.0ms
(* (* (* (sqrt (+ (fma beta alpha beta) (+ 1.0 alpha))) (sqrt (+ (fma beta alpha beta) (+ 1.0 alpha)))) (sqrt (+ (fma beta alpha beta) (+ 1.0 alpha)))) (/ (* (* (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha))) (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha)))) (sqrt (+ (fma alpha beta beta) (+ 1.0 alpha)))) (* (* (+ (+ alpha 2) beta) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta))))

prune3.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.7b
(/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2)))
0.1b
(/ (/ (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2))) 1) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
0.0b
(/ (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2))) 1) (+ (+ alpha beta) (* 2 1)))
0.0b
(+ (fma alpha beta alpha) (+ 1.0 beta))

rewrite155.0ms

Algorithm
rewrite-expression-head
Counts
4 → 463
Calls

4 calls. Slowest were:

65.0ms
(/ (/ (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2))) 1) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
36.0ms
(/ (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2))) 1) (+ (+ alpha beta) (* 2 1)))
24.0ms
(/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2)))

series268.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

103.0ms
(/ (/ (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2))) 1) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
86.0ms
(/ (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2))) 1) (+ (+ alpha beta) (* 2 1)))
58.0ms
(/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2)))
21.0ms
(+ (fma alpha beta alpha) (+ 1.0 beta))

simplify1.7m

Counts
703 → 475
Calls

703 calls. Slowest were:

820.0ms
(/ (/ (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (sqrt (+ beta (+ alpha 2)))) 1) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
721.0ms
(/ (/ (* (* (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2))) 1) (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2))) 1)) (pow (/ (+ (fma alpha beta alpha) (+ 1.0 beta)) (+ beta (+ alpha 2))) 1)) (* (* (+ (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (* (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* 2 1)) 1.0)) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
687.0ms
(/ (/ (pow (/ (cbrt (+ (fma alpha beta alpha) (+ 1.0 beta))) (cbrt (+ beta (+ alpha 2)))) 1) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune6.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes113.0ms

Accuracy

51.9% (1.1b remaining)

Error of 2.3b against oracle of 1.1b and baseline of 3.5b

bsearch106.0ms