Average Error: 57.8 → 52.4
Time: 7.1m
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}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) = -\infty:\\ \;\;\;\;\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + \sqrt{\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M} \cdot \sqrt{M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)}\right) \cdot \frac{\frac{c0}{2}}{w}\\ \mathbf{elif}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 5.2240564334301505 \cdot 10^{-248}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{\sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} \cdot \sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \left(\sqrt[3]{\sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} \cdot \sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt[3]{\sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} \cdot \sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}\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 (* (/ 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))))) < -inf.0

    1. Initial program 61.2

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

    2. Initial simplification55.1

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

    4. Applied associate-*r*55.2

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

    6. Applied sqrt-prod44.7

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

    if -inf.0 < (* (/ 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))))) < 5.2240564334301505e-248

    1. Initial program 25.1

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

    if 5.2240564334301505e-248 < (* (/ 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)))))

    1. Initial program 61.5

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

    2. Initial simplification55.1

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

    4. Applied associate-*r*55.4

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

    6. Applied add-sqr-sqrt56.0

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

    8. Applied add-cube-cbrt56.1

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

  4. Final simplification52.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) = -\infty:\\ \;\;\;\;\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) + \sqrt{\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M} \cdot \sqrt{M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)}\right) \cdot \frac{\frac{c0}{2}}{w}\\ \mathbf{elif}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 5.2240564334301505 \cdot 10^{-248}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{\sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} \cdot \sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \left(\sqrt[3]{\sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} \cdot \sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)} \cdot \sqrt[3]{\sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} \cdot \sqrt{\sqrt{\left(\frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - M\right) \cdot \left(M + \frac{d}{D} \cdot \left(\frac{d}{D} \cdot \frac{\frac{c0}{h}}{w}\right)\right)}} + \frac{\frac{c0}{h}}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}\right)\right) \cdot \frac{\frac{c0}{2}}{w}\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 
(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: 6.7m)Debug log

start1.2s

Algorithm
intervals

setup536.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.4b

localize78.0ms

Local error

Found 4 expressions with local error:

25.6b
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
13.7b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
13.7b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
13.7b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Counts
4 → 145
Calls

4 calls. Slowest were:

46.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
18.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
17.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

series712.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

444.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
110.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
84.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
75.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

simplify35.7s

Counts
179 → 157
Calls

179 calls. Slowest were:

577.0ms
(* (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))))) D)
509.0ms
(/ (* c0 (pow d 2)) (* (pow D 2) (* w h)))
496.0ms
(/ (* c0 (pow d 2)) (* (pow D 2) (* w h)))

prune3.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 50.4b

localize42.0ms

Local error

Found 4 expressions with local error:

25.6b
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
25.6b
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
25.6b
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
13.7b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Counts
4 → 227
Calls

4 calls. Slowest were:

38.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
25.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
22.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))

series1.5s

Counts
4 → 12
Calls

4 calls. Slowest were:

521.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
459.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
426.0ms
(+ (sqrt (* (+ M (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
106.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

simplify1.4m

Counts
369 → 239
Calls

369 calls. Slowest were:

822.0ms
(+ (* (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)))) (* w 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))) (* (/ c0 h) (* d (/ d D)))))
771.0ms
(+ (* (sqrt (* (- (* M M) (* (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))) (- (pow (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) 3) (pow M 3)))) (* w (* D 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))))) (* (/ c0 h) (* d d))))
756.0ms
(+ (* (sqrt (* (+ (pow M 3) (pow (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) 3)) (- (pow (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) 3) (pow M 3)))) (* w (* 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))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (+ (* M M) (* (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))) (* (/ c0 h) (* d d))))

prune8.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 50.4b

localize49.0ms

Local error

Found 4 expressions with local error:

27.5b
(+ (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
13.7b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
13.7b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
13.2b
(sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Counts
4 → 136
Calls

4 calls. Slowest were:

22.0ms
(+ (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
17.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
13.0ms
(sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))

series1.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

434.0ms
(sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))
434.0ms
(+ (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
96.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))
81.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

simplify32.6s

Counts
170 → 148
Calls

170 calls. Slowest were:

835.0ms
(+ (* (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)))) (* w 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))) (* (/ c0 h) (* (/ d D) d))))
656.0ms
(+ (* (sqrt (* (+ (pow M 3) (pow (* (* (/ (/ c0 h) w) (/ d D)) (/ d D)) 3)) (- (pow (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) 3) (pow M 3)))) 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))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D)))) (+ (* M M) (* (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))) (* (/ (/ c0 h) w) (* d (/ d D)))))
582.0ms
(+ (* (sqrt (* (- (* M M) (* (* (* (/ (/ c0 h) w) (/ d D)) (/ d D)) (* (* (/ (/ c0 h) w) (/ d D)) (/ d D)))) (- (pow (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) 3) (pow M 3)))) (* w (* D 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))))) (* (/ c0 h) (* d d))))

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 49.1b

localize26.0ms

Local error

Found 4 expressions with local error:

32.9b
(+ (* (sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))) (sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
18.0b
(sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))
18.0b
(sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))
13.7b
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Counts
4 → 639
Calls

4 calls. Slowest were:

116.0ms
(+ (* (sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))) (sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
21.0ms
(sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))
20.0ms
(sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))

series1.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

454.0ms
(+ (* (sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))) (sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))) (* (/ (/ c0 h) w) (* (/ d D) (/ d D))))
242.0ms
(sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))
242.0ms
(sqrt (sqrt (* (+ M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (- (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M))))
98.0ms
(* (/ (/ c0 h) w) (* (/ d D) (/ d D)))

simplify3.5m

Counts
1177 → 651
Calls

1177 calls. Slowest were:

628.0ms
(+ (* (* (sqrt (sqrt (* (- (* M M) (* (* (* (/ (/ c0 h) w) (/ d D)) (/ d D)) (* (* (/ (/ c0 h) w) (/ d D)) (/ d D)))) (- (pow (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) 3) (pow M 3))))) (sqrt (sqrt (* (- (* M M) (* (* (* (/ (/ c0 h) w) (/ d D)) (/ d D)) (* (* (/ (/ c0 h) w) (/ d D)) (/ d D)))) (- (pow (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) 3) (pow M 3)))))) D) (* (* (sqrt (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)))))) (sqrt (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))))))) (* (/ (/ c0 h) w) (* d (/ d D)))))
627.0ms
(* (* (sqrt (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)))))) (sqrt (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))))))) w)
614.0ms
(* (* (sqrt (sqrt (* (- M (* (* (/ (/ c0 h) w) (/ d D)) (/ d D))) (+ (* (/ (/ c0 h) w) (* (/ d D) (/ d D))) M)))) (sqrt (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 D))

prune21.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 47.6b

regimes1.9s

Accuracy

26.1% (4.7b remaining)

Error of 52.4b against oracle of 47.7b and baseline of 54.1b

bsearch16.0ms