Average Error: 32.5 → 8.1
Time: 1.8m
Precision: 64
Internal Precision: 128
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.1664794702931526 \cdot 10^{+48} \lor \neg \left(t \le 6.959105460343026 \cdot 10^{-26}\right):\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{2}{\left(\left(\left(\sin k \cdot t\right) \cdot \frac{t}{\ell}\right) \cdot \sin k\right) \cdot \left(1 + \left({\left(\frac{k}{t}\right)}^{2} + 1\right)\right)}\right) \cdot \cos k\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\frac{t \cdot t}{\frac{\ell}{2}} + \frac{k}{\frac{\ell}{k}}\right) \cdot \left(\sin k \cdot \sin k\right)} \cdot \left(\cos k \cdot \frac{\ell}{t}\right)\\ \end{array}\]

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 < -4.1664794702931526e+48 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 -4.1664794702931526e+48 < 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*33.5

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

    9. Applied tan-quot33.5

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

    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 21.1

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

    16. Simplified16.4

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

  4. Final simplification8.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.1664794702931526 \cdot 10^{+48} \lor \neg \left(t \le 6.959105460343026 \cdot 10^{-26}\right):\\ \;\;\;\;\left(\frac{\ell}{t} \cdot \frac{2}{\left(\left(\left(\sin k \cdot t\right) \cdot \frac{t}{\ell}\right) \cdot \sin k\right) \cdot \left(1 + \left({\left(\frac{k}{t}\right)}^{2} + 1\right)\right)}\right) \cdot \cos k\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\frac{t \cdot t}{\frac{\ell}{2}} + \frac{k}{\frac{\ell}{k}}\right) \cdot \left(\sin k \cdot \sin k\right)} \cdot \left(\cos k \cdot \frac{\ell}{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019016 
(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: 1.7m)Debug log

sample459.0ms

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)

simplify119.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
119.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize44.0ms

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))

rewrite88.0ms

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×flip-+
4×flip3-+
4×cbrt-undiv
4×pow-to-exp
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 → 112
Calls
4 calls:
Slowest
55.0ms
(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
20.0ms
(* (* (/ (pow t 3) (* l l)) (sin k)) (tan k))
6.0ms
(/ (pow t 3) (* l l))
5.0ms
(* (/ (pow t 3) (* l l)) (sin k))

series688.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
398.0ms
(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
190.0ms
(* (* (/ (pow t 3) (* l l)) (sin k)) (tan k))
83.0ms
(* (/ (pow t 3) (* l l)) (sin k))
17.0ms
(/ (pow t 3) (* l l))

simplify15.3s

Counts
98 → 124
Calls
98 calls:
Slowest
1.0s
(* (* l l) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
680.0ms
(- (+ 1 (pow (/ k t) 2)) 1)
660.0ms
(* (* l l) (- (+ 1 (pow (/ k t) 2)) 1))
618.0ms
(* (* (* (pow t 3) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
586.0ms
(* (cos k) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.1b

localize24.0ms

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
3×*-commutative
2×div-inv
1×associate-/l*
1×distribute-lft-in
1×frac-2neg
1×clear-num
1×distribute-rgt-in
Counts
4 → 107
Calls
4 calls:
Slowest
78.0ms
(* (* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
40.0ms
(* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k))
4.0ms
(* (/ (* t t) l) (sin k))
2.0ms
(/ (* t t) l)

series617.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
361.0ms
(* (* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
170.0ms
(* (* (/ t l) (* (/ (* t t) l) (sin k))) (tan k))
76.0ms
(* (/ (* t t) l) (sin k))
10.0ms
(/ (* t t) l)

simplify19.9s

Counts
100 → 119
Calls
100 calls:
Slowest
695.0ms
(* (cos k) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
672.0ms
(* l (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
618.0ms
(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
610.0ms
(* (* l l) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
594.0ms
(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.4b

localize20.0ms

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)))

rewrite167.0ms

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
3×*-commutative
2×div-inv
1×distribute-lft-in
1×frac-2neg
1×associate-/r*
1×clear-num
1×distribute-rgt-in
Counts
4 → 131
Calls
4 calls:
Slowest
118.0ms
(* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
20.0ms
(* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k))
20.0ms
(/ 2 (* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))
5.0ms
(* (/ t (/ l t)) (sin k))

series866.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
373.0ms
(* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
226.0ms
(/ 2 (* (* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))
176.0ms
(* (* (/ t l) (* (/ t (/ l t)) (sin k))) (tan k))
91.0ms
(* (/ t (/ l t)) (sin k))

simplify26.9s

Counts
123 → 143
Calls
123 calls:
Slowest
773.0ms
(* (/ l t) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
747.0ms
(* (* (* (/ t l) (* t (sin k))) (tan k)) (- (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (* 1 1)))
709.0ms
(* (cos k) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
696.0ms
(* (/ l t) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
673.0ms
(- (+ 1 (pow (/ k t) 2)) 1)

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.9b

localize26.0ms

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)))

rewrite96.0ms

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×flip-+
4×*-commutative
4×flip3-+
2×div-inv
1×distribute-lft-in
1×distribute-rgt-in
Counts
4 → 91
Calls
4 calls:
Slowest
41.0ms
(* (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (* (/ l t) (cos k)))
36.0ms
(* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
12.0ms
(* (* (/ t l) (* t (sin k))) (sin k))
5.0ms
(* (/ t l) (* t (sin k)))

series538.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(* (/ 2 (* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (* (/ l t) (cos k)))
182.0ms
(* (* (* (/ t l) (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
92.0ms
(* (/ t l) (* t (sin k)))
81.0ms
(* (* (/ t l) (* t (sin k))) (sin k))

simplify11.9s

Counts
69 → 103
Calls
69 calls:
Slowest
993.0ms
(- (+ 1 (pow (/ k t) 2)) 1)
681.0ms
(* (* (* (/ t l) (/ t l)) (/ t l)) (* (* (* t (sin k)) (* t (sin k))) (* t (sin k))))
660.0ms
(/ 2 (* (* (* t (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1)))
576.0ms
(* (* (* t (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
564.0ms
(* (* (* (/ 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))))

prune1.7s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.0b

regimes579.0ms

Accuracy

68.1% (2.8b remaining)

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

bsearch994.0ms

end0.0ms

sample15.4s

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)