Details

Time bar (total: 15.8s)

sample45.0ms

Algorithm
intervals
Results
17.0ms299×body80valid
7.0ms112×body80nan

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28018
317218
440518
5124618
6485918
done500018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(* 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))))
5.5b
(/ (* M D) (* 2.0 d))
7.1b
(* (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)))))
2.0ms
(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))

series1.5s

Counts
4 → 12
Calls
4 calls:
407.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
373.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
683.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify765.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (247.0ms)

IterNodesCost
02362311
16102083
223081927
done50001927

prune406.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.2b

localize14.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.5b
(/ (* M D) (* 2.0 d))

rewrite31.0ms

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:
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
7.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.0ms
(/ (* M D) (* 2.0 d))

series2.0s

Counts
4 → 12
Calls
4 calls:
874.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
720.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
373.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
32.0ms
(/ (* M D) (* 2.0 d))

simplify744.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (201.0ms)

IterNodesCost
02241799
15601636
223121480
done50001480

prune351.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize20.0ms

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)))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))
5.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
16×add-sqr-sqrt
12×div-exp
10×*-un-lft-identity
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp sqrt-prod
4×add-log-exp
3×times-frac associate-*r* div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 90
Calls
4 calls:
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)))
5.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.2s

Counts
4 → 12
Calls
4 calls:
367.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
32.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
727.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify697.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (142.0ms)

IterNodesCost
01751958
14461574
217571384
done50001384

prune365.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize20.0ms

Local error

Found 4 expressions with local error:

5.4b
(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.5b
(/ (* 2.0 d) (* M D))
5.5b
(/ (* M D) (* 2.0 d))
5.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
16×add-sqr-sqrt
12×div-exp
10×*-un-lft-identity
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp sqrt-prod
4×add-log-exp
3×times-frac associate-*r* div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 90
Calls
4 calls:
7.0ms
(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.0ms
(/ (* 2.0 d) (* M D))
4.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.1s

Counts
4 → 12
Calls
4 calls:
293.0ms
(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
27.0ms
(/ (* 2.0 d) (* M D))
27.0ms
(/ (* M D) (* 2.0 d))
710.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify846.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (192.0ms)

IterNodesCost
01982010
15261850
223791658
done50001658

prune349.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

regimes823.0ms

Accuracy

0% (1.8b remaining)

Error of 9.4b against oracle of 7.6b and baseline of 9.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02434
13134
done3134

end0.0ms

sample1.2s

Algorithm
intervals
Results
516.0ms9351×body80valid
184.0ms3125×body80nan