Average Error: 58.2 → 33.6
Time: 1.2m
Precision: 64
Internal Precision: 128
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[0\]

Error

Bits error versus c0

Bits error versus w

Bits error versus h

Bits error versus D

Bits error versus d

Bits error versus M

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.2

    \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

  2. Taylor expanded around -inf 35.1

    \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{0}\]
  3. Using strategy rm

  4. Applied mul033.6

    \[\leadsto \color{blue}{0}\]

  5. Final simplification33.6

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019007 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))))

Details

Time bar (total: 1.2m)Debug log

sample645.0ms

Algorithm
intervals

simplify414.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

413.0ms
(* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.7b

localize91.0ms

Local error

Found 4 expressions with local error:

29.0b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

74.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
11.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
10.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))

series766.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

543.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
81.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
72.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
69.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))

simplify12.2s

Counts
39 → 77
Calls

39 calls. Slowest were:

937.0ms
(+ (* (* c0 (* d d)) (sqrt (+ (* (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D))))) (+ (* (* M M) (* M M)) (* (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))))) (* (* (* w h) (* D D)) (sqrt (- (pow (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) 3) (pow (* M M) 3)))))
666.0ms
(+ (* (* c0 (* d d)) (sqrt (+ (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))) (* (* (* w h) (* D D)) (sqrt (- (* (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D))))) (* (* M M) (* M M))))))
662.0ms
(* (* (* w h) (* D D)) (sqrt (+ (* (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D))))) (+ (* (* M M) (* M M)) (* (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 33.2b

localize6.0ms

Local error

Found 1 expressions with local error:

4.9b
(* (/ c0 (* 2 w)) 0)

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 14
Calls

1 calls. Slowest were:

5.0ms
(* (/ c0 (* 2 w)) 0)

series3.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

3.0ms
(* (/ c0 (* 2 w)) 0)

simplify15.0ms

Counts
6 → 17
Calls

6 calls. Slowest were:

6.0ms
(* (cbrt (/ c0 (* 2 w))) (cbrt (/ c0 (* 2 w))))
5.0ms
(sqrt (/ c0 (* 2 w)))
1.0ms
(* c0 0)

prune234.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 31.5b

localize0.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune24.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 31.5b

localize40.0ms

Local error

Found 4 expressions with local error:

29.0b
(+ (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))
13.6b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
13.6b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
13.6b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Counts
4 → 145
Calls

4 calls. Slowest were:

39.0ms
(+ (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))
23.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
18.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

series786.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

474.0ms
(+ (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))
114.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
105.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
93.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

simplify34.1s

Counts
179 → 157
Calls

179 calls. Slowest were:

808.0ms
(/ (* c0 (pow d 2)) (* (pow D 2) (* w h)))
621.0ms
(+ (* (* (/ c0 h) (* d d)) (sqrt (* (+ (* M M) (- (* (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (* M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))))) (+ (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))) (* (* w (* D D)) (sqrt (* (+ (pow M 3) (pow (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) 3)) (- (* (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (* M M))))))
605.0ms
(* D (sqrt (* (- M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (+ (* (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (+ (* M M) (* (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))))

prune3.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 31.4b

regimes1.1s

Accuracy

0% (2.5b remaining)

Error of 33.6b against oracle of 31.1b and baseline of 33.6b

bsearch0.0ms

end0.0ms

sample17.9s

Algorithm
intervals