Details

Time bar (total: 13.9s)

sample48.0ms

Algorithm
intervals
Results
16.0ms295×body80valid
6.0ms110×body80nan

simplify790.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01718
13618
28018
317318
442718
5133718
done500018

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize15.0ms

Local error

Found 4 expressions with local error:

3.3b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.8b
(/ (* M D) (* 2.0 d))
10.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite35.0ms

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:
9.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
15.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
425.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
448.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
30.0ms
(/ (* M D) (* 2.0 d))
739.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify864.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (223.0ms)

IterNodesCost
02362311
16142085
226321927
done50001927

prune435.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.6b

localize17.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.4b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.8b
(/ (* M D) (* 2.0 d))

rewrite35.0ms

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:
7.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
11.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
8.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.0ms
(/ (* M D) (* 2.0 d))

series2.0s

Counts
4 → 12
Calls
4 calls:
829.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
803.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
369.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
37.0ms
(/ (* M D) (* 2.0 d))

simplify767.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (186.0ms)

IterNodesCost
02241799
15661636
224571480
done50011480

prune362.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.2b

localize23.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.4b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
6.8b
(/ (* M D) (* 2.0 d))
6.8b
(/ (* M D) (* 2.0 d))

rewrite41.0ms

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:
17.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
7.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
743.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
436.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
41.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))

simplify989.0ms

Counts
148 → 148
Iterations

Useful iterations: 2 (414.0ms)

IterNodesCost
02654074
17782623
225002341
done50012341

prune332.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.0b

localize22.0ms

Local error

Found 4 expressions with local error:

5.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
6.2b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.8b
(/ (* M D) (* 2.0 d))
6.8b
(/ (* M D) (* 2.0 d))

rewrite20.0ms

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:
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
396.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
778.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
35.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(/ (* M D) (* 2.0 d))

simplify603.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (146.0ms)

IterNodesCost
01761862
14761695
219981277
done50001277

prune342.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.0b

regimes922.0ms

Accuracy

0% (1.3b remaining)

Error of 8.9b against oracle of 7.5b and baseline of 8.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02032
12532
done2532

end0.0ms

sample1.1s

Algorithm
intervals
Results
505.0ms9301×body80valid
168.0ms2986×body80nan