Average Error: 52.5 → 38.9
Time: 2.0m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{(\left(\alpha + \left(\beta + i\right)\right) \cdot i + \left(\alpha \cdot \beta\right))_*}{(i \cdot 2 + \left(\beta + \alpha\right))_* \cdot (i \cdot 2 + \left(\beta + \alpha\right))_*}}{\sqrt{(\left((i \cdot 2 + \left(\beta + \alpha\right))_*\right) \cdot \left((i \cdot 2 + \left(\beta + \alpha\right))_*\right) + \left(-1.0\right))_*}} \cdot \frac{(\left(\beta + i\right) \cdot i + \left(\alpha \cdot i\right))_*}{\sqrt{(\left((2 \cdot i + \alpha)_* + \beta\right) \cdot \left((2 \cdot i + \alpha)_* + \beta\right) + \left(-1.0\right))_*}}\]

Error

Bits error versus alpha

Bits error versus beta

Bits error versus i

Derivation

  1. Initial program 52.5

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

  3. Applied associate-/l*38.8

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

  5. Applied add-sqr-sqrt38.8

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

  6. Applied div-inv38.8

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

  7. Applied times-frac38.9

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

  8. Simplified38.9

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

  9. Simplified38.9

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

  10. Final simplification38.9

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

Reproduce

herbie shell --seed 2019022 +o rules:numerics
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/4"
  :pre (and (> alpha -1) (> beta -1) (> i 1))
  (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))

Details

Time bar (total: 2.0m)Debug log

sample72.0ms

Algorithm
intervals
Results
48.0ms256×body80valid
10.0ms256×pre80true

simplify252.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
251.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.8b

localize55.0ms

Local error

Found 4 expressions with local error:

45.4b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
37.0b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
48×flip-+
48×flip3-+
44×times-frac
42×associate-/r/
38×add-exp-log
38×add-cbrt-cube
32×frac-times
28×associate-*r/
25×add-cube-cbrt
25×*-un-lft-identity
25×add-sqr-sqrt
16×associate-*l/
14×associate-/l*
13×div-exp
13×cbrt-undiv
11×pow1
10×cbrt-unprod
10×prod-exp
9×associate-/l/
6×div-inv
6×associate-*r*
4×add-log-exp
4×log1p-expm1-u
4×associate-*l*
4×associate-/r*
4×expm1-log1p-u
2×*-commutative
2×pow-prod-down
2×distribute-lft-in
2×frac-2neg
2×clear-num
2×distribute-rgt-in
1×flip--
1×pow-prod-up
1×flip3--
1×pow-plus
1×pow2
Counts
4 → 178
Calls
4 calls:
Slowest
60.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
21.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
15.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
11.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
777.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
163.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
84.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
54.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify43.7s

Counts
191 → 190
Calls
191 calls:
Slowest
798.0ms
(* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i)))
797.0ms
(* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i)))
732.0ms
(* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))
647.0ms
(/ (* (- (+ alpha beta) (* 2 i)) (+ (* (+ alpha beta) (+ alpha beta)) (- (* (* 2 i) (* 2 i)) (* (+ alpha beta) (* 2 i))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
616.0ms
(cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 36.9b

localize10.0ms

Local error

Found 4 expressions with local error:

38.8b
(/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.0b
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
2.4b
(/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
39×add-cube-cbrt
39×*-un-lft-identity
39×add-sqr-sqrt
34×add-exp-log
34×add-cbrt-cube
21×associate-/r/
20×flip-+
20×flip3-+
16×associate-/l*
16×div-exp
16×cbrt-undiv
15×associate-/r*
13×div-inv
11×associate-/l/
9×pow1
8×frac-times
6×associate-*r/
4×add-log-exp
4×log1p-expm1-u
4×cbrt-unprod
4×prod-exp
4×associate-*l/
4×expm1-log1p-u
3×associate-*l*
3×associate-*r*
3×frac-2neg
3×clear-num
1×flip--
1×pow-prod-up
1×*-commutative
1×pow-prod-down
1×flip3--
1×pow-plus
1×distribute-lft-in
1×distribute-rgt-in
1×pow2
Counts
4 → 187
Calls
4 calls:
Slowest
28.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
19.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
17.0ms
(/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
12.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
717.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
162.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
140.0ms
(/ (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
51.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify42.0s

Counts
208 → 199
Calls
208 calls:
Slowest
1.2s
(* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))
1.1s
(* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))
922.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
874.0ms
(/ (/ i (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) 1)
870.0ms
(* (+ (+ alpha beta) (* 2 i)) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))

prune3.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.9b

localize76.0ms

Local error

Found 4 expressions with local error:

38.9b
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
37.2b
(sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0)))
37.2b
(sqrt (fma (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)) (- 1.0)))
33.2b
(/ (fma (+ i beta) i (* i alpha)) (sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
23×add-cube-cbrt
23×*-un-lft-identity
21×times-frac
18×sqrt-prod
11×add-exp-log
11×add-cbrt-cube
7×associate-/r*
6×associate-/l*
4×add-log-exp
4×log1p-expm1-u
4×pow1
4×expm1-log1p-u
3×div-exp
3×cbrt-undiv
2×div-inv
2×pow1/2
2×frac-2neg
2×clear-num
2×rem-sqrt-square
1×cbrt-unprod
1×prod-exp
Counts
4 → 92
Calls
4 calls:
Slowest
5.0ms
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
4.0ms
(/ (fma (+ i beta) i (* i alpha)) (sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0))))
1.0ms
(sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0)))
1.0ms
(sqrt (fma (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)) (- 1.0)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
253.0ms
(/ (fma (+ i beta) i (* i alpha)) (sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0))))
108.0ms
(sqrt (fma (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)) (- 1.0)))
101.0ms
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
89.0ms
(sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0)))

simplify9.4s

Counts
79 → 104
Calls
79 calls:
Slowest
597.0ms
(sqrt (fma (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)) (- 1.0)))
594.0ms
(sqrt (sqrt (fma (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)) (- 1.0))))
484.0ms
(sqrt (* (cbrt (fma (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)) (- 1.0))) (cbrt (fma (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)) (- 1.0)))))
411.0ms
(/ (* (* (fma (+ i beta) i (* i alpha)) (fma (+ i beta) i (* i alpha))) (fma (+ i beta) i (* i alpha))) (* (* (sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0))) (sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0)))) (sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0)))))
410.0ms
(- (log (fma (+ (+ i beta) alpha) i (* beta alpha))) (log (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)))))

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 36.9b

localize18.0ms

Local error

Found 4 expressions with local error:

38.9b
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
38.9b
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
38.9b
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
37.2b
(sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
19×add-cbrt-cube
12×add-sqr-sqrt
11×add-cube-cbrt
11×*-un-lft-identity
9×associate-/l*
9×times-frac
6×div-exp
6×cbrt-undiv
4×add-log-exp
4×log1p-expm1-u
4×pow1
4×expm1-log1p-u
3×div-inv
3×cbrt-unprod
3×sqrt-prod
3×prod-exp
3×frac-2neg
3×associate-/r*
3×clear-num
1×pow1/2
1×rem-sqrt-square
Counts
4 → 83
Calls
4 calls:
Slowest
14.0ms
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
10.0ms
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
6.0ms
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
1.0ms
(sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(sqrt (fma (+ (fma 2 i alpha) beta) (+ (fma 2 i alpha) beta) (- 1.0)))
75.0ms
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
74.0ms
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))
61.0ms
(/ (fma (+ (+ i beta) alpha) i (* beta alpha)) (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta))))

simplify5.4s

Counts
55 → 95
Calls
55 calls:
Slowest
429.0ms
(- (log (fma (+ (+ i beta) alpha) i (* beta alpha))) (log (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)))))
395.0ms
(- (log (fma (+ (+ i beta) alpha) i (* beta alpha))) (log (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)))))
389.0ms
(- (log (fma (+ (+ i beta) alpha) i (* beta alpha))) (log (* (fma i 2 (+ alpha beta)) (fma i 2 (+ alpha beta)))))
311.0ms
(+ (* 2 (* (sqrt -1.0) (* i alpha))) (+ (sqrt (- 1.0)) (* 2 (* (sqrt -1.0) (pow i 2)))))
172.0ms
(- (log (fma (+ (+ i beta) alpha) i (* beta alpha))) (+ (log (fma i 2 (+ alpha beta))) (log (fma i 2 (+ alpha beta)))))

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 36.9b

regimes269.0ms

Accuracy

0% (2.8b remaining)

Error of 38.9b against oracle of 36.1b and baseline of 38.9b

bsearch4.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.9s8000×body80valid
315.0ms8000×pre80true