Average Error: 32.5 → 8.1
Time: 1.8m
Precision: 64
Internal Precision: 128
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.508534954191774 \cdot 10^{+47} \lor \neg \left(t \le 6.959105460343026 \cdot 10^{-26}\right):\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{2}{\left(\left(\left(\sin k \cdot t\right) \cdot \frac{t}{\ell}\right) \cdot \sin k\right) \cdot \left(1 + \left({\left(\frac{k}{t}\right)}^{2} + 1\right)\right)}\right) \cdot \cos k\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\left(t \cdot t\right) \cdot \frac{2}{\ell} + \frac{k}{\frac{\ell}{k}}\right) \cdot \left(\sin k \cdot \sin k\right)} \cdot \left(\cos k \cdot \frac{\ell}{t}\right)\\ \end{array}\]

Error

Bits error versus t

Bits error versus l

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if t < -8.508534954191774e+47 or 6.959105460343026e-26 < t

    1. Initial program 22.9

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
    2. Using strategy rm

    3. Applied cube-mult22.9

      \[\leadsto \frac{2}{\left(\left(\frac{\color{blue}{t \cdot \left(t \cdot t\right)}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    4. Applied times-frac15.9

      \[\leadsto \frac{2}{\left(\left(\color{blue}{\left(\frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\right)} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    5. Applied associate-*l*14.0

      \[\leadsto \frac{2}{\left(\color{blue}{\left(\frac{t}{\ell} \cdot \left(\frac{t \cdot t}{\ell} \cdot \sin k\right)\right)} \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
    6. Using strategy rm

    7. Applied associate-/l*7.6

      \[\leadsto \frac{2}{\left(\left(\frac{t}{\ell} \cdot \left(\color{blue}{\frac{t}{\frac{\ell}{t}}} \cdot \sin k\right)\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
    8. Using strategy rm

    9. Applied tan-quot7.6

      \[\leadsto \frac{2}{\left(\left(\frac{t}{\ell} \cdot \left(\frac{t}{\frac{\ell}{t}} \cdot \sin k\right)\right) \cdot \color{blue}{\frac{\sin k}{\cos k}}\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    10. Applied associate-*l/6.3

      \[\leadsto \frac{2}{\left(\left(\frac{t}{\ell} \cdot \color{blue}{\frac{t \cdot \sin k}{\frac{\ell}{t}}}\right) \cdot \frac{\sin k}{\cos k}\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    11. Applied associate-*r/6.3

      \[\leadsto \frac{2}{\left(\color{blue}{\frac{\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)}{\frac{\ell}{t}}} \cdot \frac{\sin k}{\cos k}\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    12. Applied frac-times3.0

      \[\leadsto \frac{2}{\color{blue}{\frac{\left(\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)\right) \cdot \sin k}{\frac{\ell}{t} \cdot \cos k}} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    13. Applied associate-*l/2.7

      \[\leadsto \frac{2}{\color{blue}{\frac{\left(\left(\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)\right) \cdot \sin k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}{\frac{\ell}{t} \cdot \cos k}}}\]

    14. Applied associate-/r/2.6

      \[\leadsto \color{blue}{\frac{2}{\left(\left(\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)\right) \cdot \sin k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \cdot \left(\frac{\ell}{t} \cdot \cos k\right)}\]
    15. Using strategy rm

    16. Applied associate-*r*2.6

      \[\leadsto \color{blue}{\left(\frac{2}{\left(\left(\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)\right) \cdot \sin k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \cdot \frac{\ell}{t}\right) \cdot \cos k}\]

    if -8.508534954191774e+47 < t < 6.959105460343026e-26

    1. Initial program 46.7

      \[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
    2. Using strategy rm

    3. Applied cube-mult46.7

      \[\leadsto \frac{2}{\left(\left(\frac{\color{blue}{t \cdot \left(t \cdot t\right)}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    4. Applied times-frac39.8

      \[\leadsto \frac{2}{\left(\left(\color{blue}{\left(\frac{t}{\ell} \cdot \frac{t \cdot t}{\ell}\right)} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    5. Applied associate-*l*38.1

      \[\leadsto \frac{2}{\left(\color{blue}{\left(\frac{t}{\ell} \cdot \left(\frac{t \cdot t}{\ell} \cdot \sin k\right)\right)} \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
    6. Using strategy rm

    7. Applied associate-/l*33.6

      \[\leadsto \frac{2}{\left(\left(\frac{t}{\ell} \cdot \left(\color{blue}{\frac{t}{\frac{\ell}{t}}} \cdot \sin k\right)\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
    8. Using strategy rm

    9. Applied tan-quot33.6

      \[\leadsto \frac{2}{\left(\left(\frac{t}{\ell} \cdot \left(\frac{t}{\frac{\ell}{t}} \cdot \sin k\right)\right) \cdot \color{blue}{\frac{\sin k}{\cos k}}\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    10. Applied associate-*l/34.0

      \[\leadsto \frac{2}{\left(\left(\frac{t}{\ell} \cdot \color{blue}{\frac{t \cdot \sin k}{\frac{\ell}{t}}}\right) \cdot \frac{\sin k}{\cos k}\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    11. Applied associate-*r/34.0

      \[\leadsto \frac{2}{\left(\color{blue}{\frac{\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)}{\frac{\ell}{t}}} \cdot \frac{\sin k}{\cos k}\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    12. Applied frac-times34.5

      \[\leadsto \frac{2}{\color{blue}{\frac{\left(\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)\right) \cdot \sin k}{\frac{\ell}{t} \cdot \cos k}} \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]

    13. Applied associate-*l/31.5

      \[\leadsto \frac{2}{\color{blue}{\frac{\left(\left(\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)\right) \cdot \sin k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}{\frac{\ell}{t} \cdot \cos k}}}\]

    14. Applied associate-/r/31.5

      \[\leadsto \color{blue}{\frac{2}{\left(\left(\frac{t}{\ell} \cdot \left(t \cdot \sin k\right)\right) \cdot \sin k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)} \cdot \left(\frac{\ell}{t} \cdot \cos k\right)}\]

    15. Taylor expanded around inf 21.2

      \[\leadsto \frac{2}{\color{blue}{2 \cdot \frac{{t}^{2} \cdot {\left(\sin k\right)}^{2}}{\ell} + \frac{{\left(\sin k\right)}^{2} \cdot {k}^{2}}{\ell}}} \cdot \left(\frac{\ell}{t} \cdot \cos k\right)\]

    16. Simplified16.4

      \[\leadsto \frac{2}{\color{blue}{\left(\sin k \cdot \sin k\right) \cdot \left(\left(t \cdot t\right) \cdot \frac{2}{\ell} + \frac{k}{\frac{\ell}{k}}\right)}} \cdot \left(\frac{\ell}{t} \cdot \cos k\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification8.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.508534954191774 \cdot 10^{+47} \lor \neg \left(t \le 6.959105460343026 \cdot 10^{-26}\right):\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{2}{\left(\left(\left(\sin k \cdot t\right) \cdot \frac{t}{\ell}\right) \cdot \sin k\right) \cdot \left(1 + \left({\left(\frac{k}{t}\right)}^{2} + 1\right)\right)}\right) \cdot \cos k\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\left(t \cdot t\right) \cdot \frac{2}{\ell} + \frac{k}{\frac{\ell}{k}}\right) \cdot \left(\sin k \cdot \sin k\right)} \cdot \left(\cos k \cdot \frac{\ell}{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (t l k)
  :name "Toniolo and Linder, Equation (10+)"
  (/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))))

Details

Time bar (total: 1.8m)Debug log

sample516.0ms

Algorithm
intervals
Results
346×(pre true 80)
180×(body real 80)
78×(body real 1280)
53×(body real 640)
19×(body real 320)
16×(body real 160)

simplify168.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
168.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize39.0ms

Local error

Found 4 expressions with local error:

16.5b
(/ (pow t 3) (* l l))
13.7b
(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
4.3b
(* (/ (pow t 3) (* l l)) (sin k))
2.5b
(* (* (/ (pow t 3) (* l l)) (sin k)) (tan k))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
44×add-exp-log
34×add-cbrt-cube
22×prod-exp
20×pow1
16×cbrt-unprod
16×associate-*l/
11×add-cube-cbrt
11×associate-*l*
11×*-un-lft-identity
11×add-sqr-sqrt
10×pow-prod-down
10×times-frac
10×frac-times
9×associate-*r*
8×tan-quot
8×div-exp
6×associate-*r/
5×associate-/l*
4×add-log-exp
4×log1p-expm1-u
4×flip-+
4×flip3-+
4×cbrt-undiv
4×pow-to-exp
4×expm1-log1p-u
3×*-commutative
3×unpow3
3×cube-mult
2×div-inv
1×distribute-lft-in
1×frac-2neg
1×associate-/r*
1×clear-num
1×distribute-rgt-in
Counts
4 → 120
Calls
4 calls:
Slowest
42.0ms
(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
13.0ms
(* (* (/ (pow t 3) (* l l)) (sin k)) (tan k))
5.0ms
(* (/ (pow t 3) (* l l)) (sin k))
3.0ms
(/ (pow t 3) (* l l))

series621.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
188.0ms
(* (* (/ (pow t 3) (* l l)) (sin k)) (tan k))
78.0ms
(* (/ (pow t 3) (* l l)) (sin k))
27.0ms
(/ (pow t 3) (* l l))

simplify16.4s

Counts
98 → 132
Calls
98 calls:
Slowest
1.3s
(* (* l l) (- (+ 1 (pow (/ k t) 2)) 1))
834.0ms
(- (+ 1 (pow (/ k t) 2)) 1)
706.0ms
(* (* l l) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
625.0ms
(* (cos k) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
609.0ms
(* (* (* l l) (cos k)) (- (+ 1 (pow (/ k t) 2)) 1))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.3b

localize44.0ms

Local error

Found 4 expressions with local error:

13.7b
(* (* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
7.7b
(/ (* t t) l)
4.8b
(* (/ (* t t) l) (sin k))
2.5b
(* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*l/
34×frac-times
29×add-exp-log
29×add-cbrt-cube
29×pow1
17×cbrt-unprod
17×prod-exp
17×pow-prod-down
16×tan-quot
14×associate-*r/
9×associate-*r*
8×flip-+
8×add-cube-cbrt
8×flip3-+
8×*-un-lft-identity
8×add-sqr-sqrt
6×associate-*l*
4×add-log-exp
4×log1p-expm1-u
4×expm1-log1p-u
3×*-commutative
2×div-inv
1×associate-/l*
1×distribute-lft-in
1×frac-2neg
1×clear-num
1×distribute-rgt-in
Counts
4 → 115
Calls
4 calls:
Slowest
81.0ms
(* (* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
32.0ms
(* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k))
9.0ms
(* (/ (* t t) l) (sin k))
4.0ms
(/ (* t t) l)

series684.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
355.0ms
(* (* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
211.0ms
(* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k))
100.0ms
(* (/ (* t t) l) (sin k))
18.0ms
(/ (* t t) l)

simplify21.8s

Counts
100 → 127
Calls
100 calls:
Slowest
1.1s
(* (* l l) (- (+ 1 (pow (/ k t) 2)) 1))
757.0ms
(- (+ 1 (pow (/ k t) 2)) 1)
693.0ms
(* (* (* l l) (cos k)) (- (+ 1 (pow (/ k t) 2)) 1))
648.0ms
(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
569.0ms
(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.7b

localize39.0ms

Local error

Found 4 expressions with local error:

13.7b
(* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
4.8b
(* (/ t (/ l t)) (sin k))
2.5b
(* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k))
0.6b
(/ 2 (* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
78×associate-*l/
63×frac-times
29×add-exp-log
29×add-cbrt-cube
29×pow1
28×tan-quot
25×associate-*r/
24×associate-/r/
17×cbrt-unprod
17×prod-exp
17×pow-prod-down
16×flip-+
16×flip3-+
9×associate-*r*
8×add-cube-cbrt
8×*-un-lft-identity
8×add-sqr-sqrt
7×associate-*l*
4×add-log-exp
4×log1p-expm1-u
4×expm1-log1p-u
3×*-commutative
2×div-inv
1×distribute-lft-in
1×frac-2neg
1×associate-/r*
1×clear-num
1×distribute-rgt-in
Counts
4 → 139
Calls
4 calls:
Slowest
78.0ms
(* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
30.0ms
(/ 2 (* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))
28.0ms
(* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k))
4.0ms
(* (/ t (/ l t)) (sin k))

series872.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
358.0ms
(* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
259.0ms
(/ 2 (* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))
188.0ms
(* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k))
66.0ms
(* (/ t (/ l t)) (sin k))

simplify29.0s

Counts
123 → 151
Calls
123 calls:
Slowest
1.2s
(* (* (* t (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
917.0ms
(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
808.0ms
(- (+ 1 (pow (/ k t) 2)) 1)
771.0ms
(* (/ l t) (- (+ 1 (pow (/ k t) 2)) 1))
737.0ms
(* (/ l t) (- (+ 1 (pow (/ k t) 2)) 1))

prune2.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.8b

localize23.0ms

Local error

Found 4 expressions with local error:

10.9b
(* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
7.4b
(* (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (* (/ l t) (cos k)))
2.0b
(* (* (/ t l) (* t (sin k))) (sin k))
1.5b
(* (/ t l) (* t (sin k)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
25×add-cbrt-cube
25×pow1
20×associate-*l/
15×associate-*l*
13×cbrt-unprod
13×prod-exp
13×pow-prod-down
8×add-cube-cbrt
8×associate-*r*
8×*-un-lft-identity
8×add-sqr-sqrt
5×associate-/r/
5×associate-*r/
5×frac-times
4×add-log-exp
4×log1p-expm1-u
4×flip-+
4×*-commutative
4×flip3-+
4×expm1-log1p-u
2×div-inv
1×distribute-lft-in
1×distribute-rgt-in
Counts
4 → 99
Calls
4 calls:
Slowest
50.0ms
(* (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (* (/ l t) (cos k)))
40.0ms
(* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
23.0ms
(* (* (/ t l) (* t (sin k))) (sin k))
11.0ms
(* (/ t l) (* t (sin k)))

series555.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(* (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (* (/ l t) (cos k)))
195.0ms
(* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
82.0ms
(* (* (/ t l) (* t (sin k))) (sin k))
80.0ms
(* (/ t l) (* t (sin k)))

simplify11.9s

Counts
69 → 111
Calls
69 calls:
Slowest
1.1s
(* (* (* t (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
658.0ms
(- (+ 1 (pow (/ k t) 2)) 1)
650.0ms
(* (* (* (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1)))) (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1)))) (* (* (* (/ l t) (cos k)) (* (/ l t) (cos k))) (* (/ l t) (cos k))))
525.0ms
(* (* (* (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1)))) (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1)))) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (cos k) (cos k)) (cos k))))
525.0ms
(* (* (* (/ t l) (/ t l)) (/ t l)) (* (* (* t (sin k)) (* t (sin k))) (* t (sin k))))

prune1.7s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.0b

regimes505.0ms

Accuracy

67.8% (2.9b remaining)

Error of 8.1b against oracle of 5.3b and baseline of 14.2b

bsearch1.0s

end0.0ms

sample15.8s

Algorithm
intervals
Results
11050×(pre true 80)
5886×(body real 80)
2081×(body real 1280)
1766×(body real 640)
871×(body real 320)
446×(body real 160)