Average Error: 25.7 → 14.1
Time: 1.7m
Precision: 64
Internal Precision: 128
\[\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;d \le -4.437468407432772 \cdot 10^{+85}:\\ \;\;\;\;\left(1 - \left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2} \cdot \frac{1}{2}\right) \cdot \frac{h}{\ell}\right) \cdot \left({\left(\frac{d}{\ell}\right)}^{\frac{1}{2}} \cdot \left(\sqrt{\frac{-1}{h}} \cdot {\left(\frac{-1}{d}\right)}^{\frac{-1}{2}}\right)\right)\\ \mathbf{elif}\;d \le -1.410505834504642 \cdot 10^{-85}:\\ \;\;\;\;\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \ell}{h \cdot \left(\frac{M}{2} \cdot \frac{D}{d}\right)}}\right) \cdot \left(\left(\sqrt{\sqrt{\frac{d}{\ell}}} \cdot \sqrt{\sqrt{\frac{d}{\ell}}}\right) \cdot \sqrt{\frac{d}{h}}\right)\\ \mathbf{elif}\;d \le 4.05717666479264 \cdot 10^{-310}:\\ \;\;\;\;\left(1 - \frac{\left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2} \cdot \frac{1}{2}\right) \cdot h}{\ell}\right) \cdot \left({\left(\frac{d}{h}\right)}^{\frac{1}{2}} \cdot \left({\left(\frac{-1}{d}\right)}^{\frac{-1}{2}} \cdot \sqrt{\frac{-1}{\ell}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \ell}{h \cdot \left(\frac{M}{2} \cdot \frac{D}{d}\right)}}\right) \cdot \left(\sqrt{d} \cdot \sqrt{d}\right)}{\sqrt{\ell} \cdot \sqrt{h}}\\ \end{array}\]

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 4 regimes

  2. if d < -4.437468407432772e+85

    1. Initial program 24.7

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

    2. Taylor expanded around -inf 17.2

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

    3. Simplified12.8

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

    if -4.437468407432772e+85 < d < -1.410505834504642e-85

    1. Initial program 16.0

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

    3. Applied associate-*r/14.3

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

    5. Applied pow114.3

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

    6. Applied pow114.3

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

    7. Applied pow-prod-down14.3

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

    8. Simplified14.1

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

    10. Applied associate-/l/11.3

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

    12. Applied add-sqr-sqrt11.3

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

    13. Applied sqrt-prod11.6

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

    if -1.410505834504642e-85 < d < 4.05717666479264e-310

    1. Initial program 37.2

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

    3. Applied associate-*r/37.0

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

    4. Taylor expanded around -inf 32.8

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

    5. Simplified30.5

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

    if 4.05717666479264e-310 < d

    1. Initial program 25.3

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

    3. Applied associate-*r/24.6

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

    5. Applied pow124.6

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

    6. Applied pow124.6

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

    7. Applied pow-prod-down24.6

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

    8. Simplified24.4

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

    10. Applied associate-/l/22.8

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

    12. Applied sqrt-div16.4

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

    13. Applied sqrt-div10.2

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

    14. Applied frac-times10.2

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

    15. Applied associate-*r/10.1

      \[\leadsto {\color{blue}{\left(\frac{\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{\ell \cdot 2}{\left(\frac{M}{2} \cdot \frac{D}{d}\right) \cdot h}}\right) \cdot \left(\sqrt{d} \cdot \sqrt{d}\right)}{\sqrt{\ell} \cdot \sqrt{h}}\right)}}^{1}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification14.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;d \le -4.437468407432772 \cdot 10^{+85}:\\ \;\;\;\;\left(1 - \left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2} \cdot \frac{1}{2}\right) \cdot \frac{h}{\ell}\right) \cdot \left({\left(\frac{d}{\ell}\right)}^{\frac{1}{2}} \cdot \left(\sqrt{\frac{-1}{h}} \cdot {\left(\frac{-1}{d}\right)}^{\frac{-1}{2}}\right)\right)\\ \mathbf{elif}\;d \le -1.410505834504642 \cdot 10^{-85}:\\ \;\;\;\;\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \ell}{h \cdot \left(\frac{M}{2} \cdot \frac{D}{d}\right)}}\right) \cdot \left(\left(\sqrt{\sqrt{\frac{d}{\ell}}} \cdot \sqrt{\sqrt{\frac{d}{\ell}}}\right) \cdot \sqrt{\frac{d}{h}}\right)\\ \mathbf{elif}\;d \le 4.05717666479264 \cdot 10^{-310}:\\ \;\;\;\;\left(1 - \frac{\left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2} \cdot \frac{1}{2}\right) \cdot h}{\ell}\right) \cdot \left({\left(\frac{d}{h}\right)}^{\frac{1}{2}} \cdot \left({\left(\frac{-1}{d}\right)}^{\frac{-1}{2}} \cdot \sqrt{\frac{-1}{\ell}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 - \frac{\frac{M}{2} \cdot \frac{D}{d}}{\frac{2 \cdot \ell}{h \cdot \left(\frac{M}{2} \cdot \frac{D}{d}\right)}}\right) \cdot \left(\sqrt{d} \cdot \sqrt{d}\right)}{\sqrt{\ell} \cdot \sqrt{h}}\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 
(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: 51.1s)Debug log

start1.7s

Algorithm
intervals

setup202.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.6b

localize85.0ms

Local error

Found 4 expressions with local error:

13.4b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
13.0b
(pow (/ d l) (/ 1 2))
10.2b
(pow (/ d h) (/ 1 2))
7.6b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Counts
4 → 91
Calls

4 calls. Slowest were:

20.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
14.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
13.0ms
(pow (/ d l) (/ 1 2))

series478.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

272.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
76.0ms
(pow (/ d l) (/ 1 2))
66.0ms
(pow (/ d h) (/ 1 2))
63.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify8.5s

Counts
71 → 103
Calls

71 calls. Slowest were:

851.0ms
(* (* 1 (pow (/ (* M D) (* 2 d)) 2)) h)
550.0ms
(+ (+ (log (/ 1 2)) (log (pow (/ (* M D) (* 2 d)) 2))) (log (/ h l)))
356.0ms
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))

prune2.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.1b

localize14.0ms

Local error

Found 4 expressions with local error:

13.0b
(pow (/ d l) (/ 1 2))
10.2b
(pow (/ d h) (/ 1 2))
7.6b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)))
7.5b
(/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)

rewrite57.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

28.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)))
21.0ms
(/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)
3.0ms
(pow (/ d l) (/ 1 2))

series498.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

250.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)))
90.0ms
(/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)
82.0ms
(pow (/ d h) (/ 1 2))
77.0ms
(pow (/ d l) (/ 1 2))

simplify7.1s

Counts
57 → 91
Calls

57 calls. Slowest were:

858.0ms
(* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))
822.0ms
(* (* 1 (pow (/ (* M D) (* 2 d)) 2)) h)
276.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)) (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l))) (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l))))

prune2.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.1b

localize52.0ms

Local error

Found 4 expressions with local error:

13.0b
(sqrt (/ d l))
11.1b
(/ (/ (* l 2) h) (* (/ M 2) (/ D d)))
10.2b
(sqrt (/ d h))
7.6b
(* (- 1 (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Counts
4 → 84
Calls

4 calls. Slowest were:

22.0ms
(* (- 1 (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))
18.0ms
(/ (/ (* l 2) h) (* (/ M 2) (/ D d)))
1.0ms
(sqrt (/ d l))

series304.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

180.0ms
(* (- 1 (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d))))) (* (sqrt (/ d l)) (sqrt (/ d h))))
63.0ms
(/ (/ (* l 2) h) (* (/ M 2) (/ D d)))
36.0ms
(sqrt (/ d h))
24.0ms
(sqrt (/ d l))

simplify7.5s

Counts
68 → 96
Calls

68 calls. Slowest were:

578.0ms
(* (* (* (- 1 (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d))))) (- 1 (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d)))))) (- 1 (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d)))))) (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l))) (* (* (sqrt (/ d h)) (sqrt (/ d h))) (sqrt (/ d h)))))
504.0ms
(* (+ (* 1 1) (+ (* (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d)))) (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d))))) (* 1 (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d))))))) (* (sqrt l) (sqrt h)))
460.0ms
(* (+ (* 1 1) (+ (* (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d)))) (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d))))) (* 1 (/ (* (/ M 2) (/ D d)) (/ (/ (* l 2) h) (* (/ M 2) (/ D d))))))) (sqrt l))

prune2.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.6b

localize28.0ms

Local error

Found 4 expressions with local error:

13.0b
(sqrt (/ d l))
10.2b
(sqrt (/ d h))
7.6b
(* (- 1 (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h)))) (* (sqrt (/ d l)) (sqrt (/ d h))))
6.2b
(/ (* l 2) (* (* (/ M 2) (/ D d)) h))

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

19.0ms
(* (- 1 (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h)))) (* (sqrt (/ d l)) (sqrt (/ d h))))
11.0ms
(/ (* l 2) (* (* (/ M 2) (/ D d)) h))
0.0ms
(sqrt (/ d l))

series295.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

194.0ms
(* (- 1 (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h)))) (* (sqrt (/ d l)) (sqrt (/ d h))))
53.0ms
(/ (* l 2) (* (* (/ M 2) (/ D d)) h))
25.0ms
(sqrt (/ d h))
23.0ms
(sqrt (/ d l))

simplify8.8s

Counts
55 → 87
Calls

55 calls. Slowest were:

687.0ms
(* (+ (* 1 1) (+ (* (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h))) (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h)))) (* 1 (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h)))))) (* (sqrt l) (sqrt h)))
667.0ms
(* (+ (* 1 1) (+ (* (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h))) (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h)))) (* 1 (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h)))))) (sqrt l))
646.0ms
(* (+ (* 1 1) (+ (* (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h))) (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h)))) (* 1 (/ (* (/ M 2) (/ D d)) (/ (* l 2) (* (* (/ M 2) (/ D d)) h)))))) (sqrt h))

prune1.6s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.1b

regimes1.7s

Accuracy

60.6% (6.0b remaining)

Error of 14.1b against oracle of 8.0b and baseline of 23.3b

bsearch5.6s