Average Error: 25.7 → 19.2
Time: 1.6m
Precision: 64
Internal Precision: 128
\[\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;h \le -1.1095464281277259 \cdot 10^{-299}:\\ \;\;\;\;\left(\sqrt[3]{1 - \frac{\frac{D}{d} \cdot \frac{M}{2}}{\frac{\frac{\ell}{h} \cdot 2}{\frac{D}{d} \cdot \frac{M}{2}}}} \cdot \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right)\right) \cdot \left(\sqrt[3]{1 - \frac{\frac{D}{d} \cdot \frac{M}{2}}{\frac{\frac{\ell}{h} \cdot 2}{\frac{D}{d} \cdot \frac{M}{2}}}} \cdot \sqrt[3]{1 - \frac{\frac{D}{d} \cdot \frac{M}{2}}{\frac{\frac{\ell}{h} \cdot 2}{\frac{D}{d} \cdot \frac{M}{2}}}}\right)\\ \mathbf{elif}\;h \le 4.086196076281636 \cdot 10^{+220}:\\ \;\;\;\;\frac{\left(1 - \frac{\frac{D}{d} \cdot \frac{M}{2}}{\frac{\frac{\ell}{h} \cdot 2}{\frac{D}{d} \cdot \frac{M}{2}}}\right) \cdot \left(\sqrt{d} \cdot \sqrt{d}\right)}{\sqrt{\ell} \cdot \sqrt{h}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left({\left(\frac{1}{\ell}\right)}^{\frac{1}{2}} \cdot \sqrt{d}\right) \cdot {\left(\frac{d}{h}\right)}^{\frac{1}{2}}\right) \cdot \left(1 - \frac{h \cdot \left({\left(\frac{D \cdot M}{d \cdot 2}\right)}^{2} \cdot \frac{1}{2}\right)}{\ell}\right)\\ \end{array}\]

Error

Bits error versus d

Bits error versus h

Bits error versus l

Bits error versus M

Bits error versus D

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if h < -1.1095464281277259e-299

    1. Initial program 25.8

      \[\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
    2. Using strategy rm

    3. Applied associate-*r/25.0

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \color{blue}{\frac{\left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot h}{\ell}}\right)\]
    4. Using strategy rm

    5. Applied associate-/l*25.7

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \color{blue}{\frac{\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}}{\frac{\ell}{h}}}\right)\]
    6. Using strategy rm

    7. Applied pow125.7

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \color{blue}{{\left(1 - \frac{\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}}{\frac{\ell}{h}}\right)}^{1}}\]

    8. Applied pow125.7

      \[\leadsto \color{blue}{{\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right)}^{1}} \cdot {\left(1 - \frac{\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}}{\frac{\ell}{h}}\right)}^{1}\]

    9. Applied pow-prod-down25.7

      \[\leadsto \color{blue}{{\left(\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \frac{\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}}{\frac{\ell}{h}}\right)\right)}^{1}}\]

    10. Simplified24.7

      \[\leadsto {\color{blue}{\left(\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\right)}}^{1}\]
    11. Using strategy rm

    12. Applied add-cube-cbrt24.8

      \[\leadsto {\left(\color{blue}{\left(\left(\sqrt[3]{1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}} \cdot \sqrt[3]{1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}}\right) \cdot \sqrt[3]{1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}}\right)} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\right)}^{1}\]

    13. Applied associate-*l*24.8

      \[\leadsto {\color{blue}{\left(\left(\sqrt[3]{1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}} \cdot \sqrt[3]{1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}}\right) \cdot \left(\sqrt[3]{1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}} \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\right)\right)}}^{1}\]

    if -1.1095464281277259e-299 < h < 4.086196076281636e+220

    1. Initial program 24.6

      \[\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
    2. Using strategy rm

    3. Applied associate-*r/24.0

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \color{blue}{\frac{\left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot h}{\ell}}\right)\]
    4. Using strategy rm

    5. Applied associate-/l*24.5

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \color{blue}{\frac{\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}}{\frac{\ell}{h}}}\right)\]
    6. Using strategy rm

    7. Applied pow124.5

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \color{blue}{{\left(1 - \frac{\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}}{\frac{\ell}{h}}\right)}^{1}}\]

    8. Applied pow124.5

      \[\leadsto \color{blue}{{\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right)}^{1}} \cdot {\left(1 - \frac{\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}}{\frac{\ell}{h}}\right)}^{1}\]

    9. Applied pow-prod-down24.5

      \[\leadsto \color{blue}{{\left(\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \frac{\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}}{\frac{\ell}{h}}\right)\right)}^{1}}\]

    10. Simplified23.6

      \[\leadsto {\color{blue}{\left(\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\right)}}^{1}\]
    11. Using strategy rm

    12. Applied sqrt-div17.4

      \[\leadsto {\left(\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \color{blue}{\frac{\sqrt{d}}{\sqrt{h}}}\right)\right)}^{1}\]

    13. Applied sqrt-div12.2

      \[\leadsto {\left(\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}\right) \cdot \left(\color{blue}{\frac{\sqrt{d}}{\sqrt{\ell}}} \cdot \frac{\sqrt{d}}{\sqrt{h}}\right)\right)}^{1}\]

    14. Applied frac-times12.2

      \[\leadsto {\left(\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}\right) \cdot \color{blue}{\frac{\sqrt{d} \cdot \sqrt{d}}{\sqrt{\ell} \cdot \sqrt{h}}}\right)}^{1}\]

    15. Applied associate-*r/12.3

      \[\leadsto {\color{blue}{\left(\frac{\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \frac{\ell}{h}}{\frac{M}{2} \cdot \frac{D}{d}}}\right) \cdot \left(\sqrt{d} \cdot \sqrt{d}\right)}{\sqrt{\ell} \cdot \sqrt{h}}\right)}}^{1}\]

    if 4.086196076281636e+220 < h

    1. Initial program 31.7

      \[\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
    2. Using strategy rm

    3. Applied associate-*r/26.9

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \color{blue}{\frac{\left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot h}{\ell}}\right)\]
    4. Using strategy rm

    5. Applied div-inv26.9

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\color{blue}{\left(d \cdot \frac{1}{\ell}\right)}}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \frac{\left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot h}{\ell}\right)\]

    6. Applied unpow-prod-down22.2

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot \color{blue}{\left({d}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{1}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right)}\right) \cdot \left(1 - \frac{\left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot h}{\ell}\right)\]

    7. Simplified22.2

      \[\leadsto \left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot \left(\color{blue}{\sqrt{d}} \cdot {\left(\frac{1}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right)\right) \cdot \left(1 - \frac{\left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot h}{\ell}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification19.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;h \le -1.1095464281277259 \cdot 10^{-299}:\\ \;\;\;\;\left(\sqrt[3]{1 - \frac{\frac{D}{d} \cdot \frac{M}{2}}{\frac{\frac{\ell}{h} \cdot 2}{\frac{D}{d} \cdot \frac{M}{2}}}} \cdot \left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right)\right) \cdot \left(\sqrt[3]{1 - \frac{\frac{D}{d} \cdot \frac{M}{2}}{\frac{\frac{\ell}{h} \cdot 2}{\frac{D}{d} \cdot \frac{M}{2}}}} \cdot \sqrt[3]{1 - \frac{\frac{D}{d} \cdot \frac{M}{2}}{\frac{\frac{\ell}{h} \cdot 2}{\frac{D}{d} \cdot \frac{M}{2}}}}\right)\\ \mathbf{elif}\;h \le 4.086196076281636 \cdot 10^{+220}:\\ \;\;\;\;\frac{\left(1 - \frac{\frac{D}{d} \cdot \frac{M}{2}}{\frac{\frac{\ell}{h} \cdot 2}{\frac{D}{d} \cdot \frac{M}{2}}}\right) \cdot \left(\sqrt{d} \cdot \sqrt{d}\right)}{\sqrt{\ell} \cdot \sqrt{h}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left({\left(\frac{1}{\ell}\right)}^{\frac{1}{2}} \cdot \sqrt{d}\right) \cdot {\left(\frac{d}{h}\right)}^{\frac{1}{2}}\right) \cdot \left(1 - \frac{h \cdot \left({\left(\frac{D \cdot M}{d \cdot 2}\right)}^{2} \cdot \frac{1}{2}\right)}{\ell}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2018360 
(FPCore (d h l M D)
  :name "Henrywood and Agarwal, Equation (12)"
  (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))

Details

Time bar (total: 45.8s)Debug log

start1.5s

Algorithm
intervals

setup217.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.1b

localize66.0ms

Local error

Found 4 expressions with local error:

15.4b
(pow (/ d l) (/ 1 2))
15.3b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
7.8b
(pow (/ d h) (/ 1 2))
6.1b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Counts
4 → 91
Calls

4 calls. Slowest were:

18.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
15.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
3.0ms
(pow (/ d l) (/ 1 2))

series488.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

209.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
104.0ms
(pow (/ d l) (/ 1 2))
88.0ms
(pow (/ d h) (/ 1 2))
87.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify7.7s

Counts
71 → 103
Calls

71 calls. Slowest were:

664.0ms
(* (* 1 (pow (/ (* M D) (* 2 d)) 2)) h)
585.0ms
(+ (+ (log (/ 1 2)) (log (pow (/ (* M D) (* 2 d)) 2))) (log (/ h l)))
355.0ms
(exp (* 1/2 (- (log (/ -1 h)) (log (/ -1 d)))))

prune2.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.8b

localize11.0ms

Local error

Found 4 expressions with local error:

15.4b
(pow (/ d l) (/ 1 2))
8.6b
(/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)
7.8b
(pow (/ d h) (/ 1 2))
6.9b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)

rewrite33.0ms

Algorithm
rewrite-expression-head
Counts
4 → 58
Calls

4 calls. Slowest were:

20.0ms
(/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)
10.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
1.0ms
(pow (/ d l) (/ 1 2))

series289.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

99.0ms
(pow (/ d l) (/ 1 2))
71.0ms
(pow (/ d h) (/ 1 2))
64.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
55.0ms
(/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)

simplify4.4s

Counts
36 → 70
Calls

36 calls. Slowest were:

776.0ms
(* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))
685.0ms
(* (* 1 (pow (/ (* M D) (* 2 d)) 2)) h)
569.0ms
(* (* 1 (pow (/ (* M D) (* 2 d)) 2)) h)

prune1.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.8b

localize12.0ms

Local error

Found 4 expressions with local error:

15.6b
(/ (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ l h))
15.4b
(pow (/ d l) (/ 1 2))
7.8b
(pow (/ d h) (/ 1 2))
6.1b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ l h))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Counts
4 → 95
Calls

4 calls. Slowest were:

27.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ l h))))
14.0ms
(/ (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ l h))
2.0ms
(pow (/ d l) (/ 1 2))

series539.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

252.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ l h))))
101.0ms
(pow (/ d h) (/ 1 2))
98.0ms
(pow (/ d l) (/ 1 2))
87.0ms
(/ (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ l h))

simplify9.2s

Counts
76 → 107
Calls

76 calls. Slowest were:

730.0ms
(/ (pow (/ (* M D) (* 2 d)) 2) (/ 1 h))
636.0ms
(/ (pow (/ (* M D) (* 2 d)) 2) (/ l h))
486.0ms
(- (+ (log (/ 1 2)) (log (pow (/ (* M D) (* 2 d)) 2))) (log (/ l h)))

prune2.5s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 15.4b

localize36.0ms

Local error

Found 4 expressions with local error:

15.4b
(sqrt (/ d l))
12.3b
(/ (* 2 (/ l h)) (* (/ M 2) (/ D d)))
7.8b
(sqrt (/ d h))
6.1b
(* (- 1 (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

24.0ms
(* (- 1 (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))
10.0ms
(/ (* 2 (/ l h)) (* (/ M 2) (/ D d)))
1.0ms
(sqrt (/ d l))

series309.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

202.0ms
(* (- 1 (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))
54.0ms
(/ (* 2 (/ l h)) (* (/ M 2) (/ D d)))
29.0ms
(sqrt (/ d l))
23.0ms
(sqrt (/ d h))

simplify7.7s

Counts
59 → 90
Calls

59 calls. Slowest were:

568.0ms
(* (- (pow 1 3) (pow (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d)))) 3)) (* (sqrt d) (sqrt (/ d h))))
518.0ms
(* (+ (* 1 1) (+ (* (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d)))) (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d))))) (* 1 (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d))))))) (sqrt h))
488.0ms
(* (+ (* 1 1) (+ (* (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d)))) (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d))))) (* 1 (/ (* (/ M 2) (/ D d)) (/ (* 2 (/ l h)) (* (/ M 2) (/ D d))))))) (* (sqrt l) (sqrt h)))

prune1.8s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 14.9b

regimes2.0s

Accuracy

52.6% (5.0b remaining)

Error of 19.2b against oracle of 14.1b and baseline of 24.8b

bsearch2.5s