Average Error: 57.9 → 53.6
Time: 2.3m
Precision: 64
Internal Precision: 128
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;D \le -4.3083809125813214 \cdot 10^{-39}:\\ \;\;\;\;\left(\sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}} \cdot \sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}}\right)\right) \cdot \frac{\frac{c0}{2}}{w}\\ \mathbf{elif}\;D \le -4.0302553235580764 \cdot 10^{-115}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(h \cdot w\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(h \cdot w\right) \cdot \left(D \cdot D\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(h \cdot w\right) \cdot \left(D \cdot D\right)}\right)\\ \mathbf{elif}\;D \le 8.857546390531178 \cdot 10^{-150}:\\ \;\;\;\;\left(\sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}} \cdot \sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}}\right)\right) \cdot \frac{\frac{c0}{2}}{w}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \sqrt{\frac{\frac{c0}{h}}{w}}\right) \cdot \sqrt{\frac{\frac{c0}{h}}{w}} - M} \cdot \sqrt{\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M} + \sqrt{\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \left(\frac{c0}{h} \cdot \frac{1}{w}\right)} \cdot \sqrt{\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \left(\frac{c0}{h} \cdot \frac{1}{w}\right)}\right) \cdot \frac{\frac{c0}{2}}{w}\\ \end{array}\]

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. Split input into 3 regimes

  2. if D < -4.3083809125813214e-39 or -4.0302553235580764e-115 < D < 8.857546390531178e-150

    1. Initial program 60.0

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

    2. Initial simplification53.6

      \[\leadsto \frac{\frac{c0}{2}}{w} \cdot \left(\sqrt{\left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)\]
    3. Using strategy rm

    4. Applied add-cube-cbrt53.7

      \[\leadsto \frac{\frac{c0}{2}}{w} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt{\left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}\right) \cdot \sqrt[3]{\sqrt{\left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}\right)}\]

    if -4.3083809125813214e-39 < D < -4.0302553235580764e-115

    1. Initial program 52.8

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

    if 8.857546390531178e-150 < D

    1. Initial program 55.3

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

    2. Initial simplification50.7

      \[\leadsto \frac{\frac{c0}{2}}{w} \cdot \left(\sqrt{\left(M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right) \cdot \left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right)} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)\]
    3. Using strategy rm

    4. Applied sqrt-prod53.5

      \[\leadsto \frac{\frac{c0}{2}}{w} \cdot \left(\color{blue}{\sqrt{M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt{\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M}} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)\]
    5. Using strategy rm

    6. Applied div-inv53.5

      \[\leadsto \frac{\frac{c0}{2}}{w} \cdot \left(\sqrt{M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt{\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M} + \color{blue}{\left(\frac{c0}{h} \cdot \frac{1}{w}\right)} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)\]
    7. Using strategy rm

    8. Applied add-sqr-sqrt53.5

      \[\leadsto \frac{\frac{c0}{2}}{w} \cdot \left(\sqrt{M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt{\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M} + \color{blue}{\sqrt{\left(\frac{c0}{h} \cdot \frac{1}{w}\right) \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt{\left(\frac{c0}{h} \cdot \frac{1}{w}\right) \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}}\right)\]
    9. Using strategy rm

    10. Applied add-sqr-sqrt53.5

      \[\leadsto \frac{\frac{c0}{2}}{w} \cdot \left(\sqrt{M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt{\color{blue}{\left(\sqrt{\frac{\frac{c0}{h}}{w}} \cdot \sqrt{\frac{\frac{c0}{h}}{w}}\right)} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M} + \sqrt{\left(\frac{c0}{h} \cdot \frac{1}{w}\right) \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt{\left(\frac{c0}{h} \cdot \frac{1}{w}\right) \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}\right)\]

    11. Applied associate-*l*53.5

      \[\leadsto \frac{\frac{c0}{2}}{w} \cdot \left(\sqrt{M + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt{\color{blue}{\sqrt{\frac{\frac{c0}{h}}{w}} \cdot \left(\sqrt{\frac{\frac{c0}{h}}{w}} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)} - M} + \sqrt{\left(\frac{c0}{h} \cdot \frac{1}{w}\right) \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt{\left(\frac{c0}{h} \cdot \frac{1}{w}\right) \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification53.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;D \le -4.3083809125813214 \cdot 10^{-39}:\\ \;\;\;\;\left(\sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}} \cdot \sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}}\right)\right) \cdot \frac{\frac{c0}{2}}{w}\\ \mathbf{elif}\;D \le -4.0302553235580764 \cdot 10^{-115}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(h \cdot w\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(h \cdot w\right) \cdot \left(D \cdot D\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(h \cdot w\right) \cdot \left(D \cdot D\right)}\right)\\ \mathbf{elif}\;D \le 8.857546390531178 \cdot 10^{-150}:\\ \;\;\;\;\left(\sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}} \cdot \left(\sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}} \cdot \sqrt[3]{\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M\right) \cdot \left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} - M\right)} + \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w}}\right)\right) \cdot \frac{\frac{c0}{2}}{w}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\left(\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \sqrt{\frac{\frac{c0}{h}}{w}}\right) \cdot \sqrt{\frac{\frac{c0}{h}}{w}} - M} \cdot \sqrt{\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \frac{\frac{c0}{h}}{w} + M} + \sqrt{\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \left(\frac{c0}{h} \cdot \frac{1}{w}\right)} \cdot \sqrt{\left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \left(\frac{c0}{h} \cdot \frac{1}{w}\right)}\right) \cdot \frac{\frac{c0}{2}}{w}\\ \end{array}\]

Reproduce

herbie shell --seed 2018360 
(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: 1.7m)Debug log

start1.1s

Algorithm
intervals

setup500.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.1b

localize38.0ms

Local error

Found 4 expressions with local error:

27.2b
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
15.4b
(sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))
15.0b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
15.0b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Counts
4 → 136
Calls

4 calls. Slowest were:

24.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
12.0ms
(sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))
9.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

series1.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

471.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
364.0ms
(sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))
110.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
103.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

simplify35.0s

Counts
170 → 148
Calls

170 calls. Slowest were:

561.0ms
(* (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))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (+ (* M M) (* (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))) D)
529.0ms
(+ (log (/ (/ c0 h) w)) (+ (log (/ d D)) (log (/ d D))))
498.0ms
(/ (* c0 (pow d 2)) (* (pow D 2) (* w h)))

prune3.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 48.2b

localize15.0ms

Local error

Found 4 expressions with local error:

15.0b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
15.0b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
15.0b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
4.3b
(/ (/ c0 h) w)

rewrite47.0ms

Algorithm
rewrite-expression-head
Counts
4 → 93
Calls

4 calls. Slowest were:

20.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
11.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
9.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

series309.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

105.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
99.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
92.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
14.0ms
(/ (/ c0 h) w)

simplify10.9s

Counts
68 → 105
Calls

68 calls. Slowest were:

609.0ms
(+ (log (/ (/ c0 h) w)) (+ (log (/ d D)) (log (/ d D))))
556.0ms
(+ (log (/ (/ c0 h) w)) (+ (log (/ d D)) (log (/ d D))))
555.0ms
(+ (log (/ (/ c0 h) w)) (+ (log (/ d D)) (log (/ d D))))

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 48.2b

localize17.0ms

Local error

Found 4 expressions with local error:

15.0b
(* (* (/ c0 h) (/ 1 w)) (* (/ d D) (/ d D)))
15.0b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
15.0b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
4.4b
(* (/ c0 h) (/ 1 w))

rewrite70.0ms

Algorithm
rewrite-expression-head
Counts
4 → 116
Calls

4 calls. Slowest were:

29.0ms
(* (* (/ c0 h) (/ 1 w)) (* (/ d D) (/ d D)))
17.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
16.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

series338.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

130.0ms
(* (* (/ c0 h) (/ 1 w)) (* (/ d D) (/ d D)))
100.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
94.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
14.0ms
(* (/ c0 h) (/ 1 w))

simplify14.2s

Counts
103 → 128
Calls

103 calls. Slowest were:

561.0ms
(* (* c0 (/ 1 w)) (* (/ d D) d))
561.0ms
(+ (log (/ (/ c0 h) w)) (+ (log (/ d D)) (log (/ d D))))
521.0ms
(/ (* c0 (pow d 2)) (* (pow D 2) (* w h)))

prune3.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 48.2b

localize19.0ms

Local error

Found 4 expressions with local error:

15.0b
(* (* (/ c0 h) (/ 1 w)) (* (/ d D) (/ d D)))
15.0b
(* (* (/ c0 h) (/ 1 w)) (* (/ d D) (/ d D)))
15.0b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
15.0b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Counts
4 → 134
Calls

4 calls. Slowest were:

25.0ms
(* (* (/ c0 h) (/ 1 w)) (* (/ d D) (/ d D)))
18.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
18.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

series429.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

131.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
121.0ms
(* (* (/ c0 h) (/ 1 w)) (* (/ d D) (/ d D)))
89.0ms
(* (* (/ c0 h) (/ 1 w)) (* (/ d D) (/ d D)))
87.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

simplify21.2s

Counts
134 → 146
Calls

134 calls. Slowest were:

605.0ms
(* (* c0 (/ 1 w)) (* d (/ d D)))
595.0ms
(+ (log (/ (/ c0 h) w)) (+ (log (/ d D)) (log (/ d D))))
581.0ms
(+ (+ (log (/ c0 h)) (log (/ 1 w))) (+ (log (/ d D)) (log (/ d D))))

prune3.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 48.2b

regimes2.1s

Accuracy

24.2% (4.9b remaining)

Error of 53.6b against oracle of 48.6b and baseline of 55.2b

bsearch2.3s