Details

Time bar (total: 17.0s)

sample44.0ms

Algorithm
intervals
Results
14.0ms296×body80valid
5.0ms90×body80nan

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01718
13618
28118
317618
442218
5117418
6457018
done500018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.7b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.7b
(/ (* M D) (* 2.0 d))
9.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
20.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
12.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
458.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
614.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
29.0ms
(/ (* M D) (* 2.0 d))
731.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify915.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (281.0ms)

IterNodesCost
02362311
15772083
222621927
done50001927

prune409.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.6b

localize14.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.7b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.7b
(/ (* M D) (* 2.0 d))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
11.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
25.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
15.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
12.0ms
(/ (* M D) (* 2.0 d))

series1.9s

Counts
4 → 12
Calls
4 calls:
402.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
731.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
734.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
29.0ms
(/ (* M D) (* 2.0 d))

simplify794.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (274.0ms)

IterNodesCost
02241799
15341636
222281480
done50001480

prune344.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize16.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.7b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (* M D) (* 2.0 d))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
352×add-exp-log
173×prod-exp
125×div-exp
75×pow-exp
37×add-cbrt-cube
15×pow-to-exp
11×cbrt-undiv cbrt-unprod
10×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
5×pow1 times-frac associate-/r* sqrt-prod
4×add-log-exp
3×frac-2neg clear-num div-inv associate-/l*
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 136
Calls
4 calls:
12.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
40.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
15.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
411.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
725.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
29.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))

simplify854.0ms

Counts
148 → 148
Iterations

Useful iterations: 2 (281.0ms)

IterNodesCost
02654074
15672623
221672341
done50002341

prune336.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize20.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
5.5b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (* M D) (* 2.0 d))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
33×add-cbrt-cube
20×div-exp
19×prod-exp
10×cbrt-undiv
9×cbrt-unprod
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
5×pow1 times-frac pow-exp associate-/r*
4×add-log-exp
3×frac-2neg clear-num sqrt-prod div-inv associate-/l*
2×sqrt-div
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 84
Calls
4 calls:
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
16.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
12.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
407.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
727.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
29.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))

simplify714.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (212.0ms)

IterNodesCost
01761862
14401695
219151277
done50011277

prune299.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

regimes835.0ms

Accuracy

0% (1.3b remaining)

Error of 8.2b against oracle of 6.9b and baseline of 8.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02032
12532
done2532

end0.0ms

sample1.2s

Algorithm
intervals
Results
462.0ms9351×body80valid
168.0ms3152×body80nan