Details

Time bar (total: 24.4s)

sample108.0ms

Algorithm
intervals
Results
34.0ms297×body80valid
23.0ms104×body80nan

simplify1.0s

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize30.0ms

Local error

Found 4 expressions with local error:

2.0b
(* 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))))
7.4b
(/ (* M D) (* 2.0 d))
10.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite86.0ms

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:
18.0ms
(* 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))))
13.0ms
(/ (* M D) (* 2.0 d))
45.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
599.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
577.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
30.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.3s

Counts
125 → 125

prune646.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.6b

localize31.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.9b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
7.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
7.4b
(/ (* M D) (* 2.0 d))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 128
Calls
4 calls:
55.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
9.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
43.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
18.0ms
(/ (* M D) (* 2.0 d))

series2.7s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
613.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
34.0ms
(/ (* M D) (* 2.0 d))

simplify1.3s

Counts
140 → 140

prune564.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.5b

localize52.0ms

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)) (/ 1 l))))
6.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
7.4b
(/ (* M D) (* 2.0 d))
7.4b
(/ (* M D) (* 2.0 d))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
14×add-sqr-sqrt
12×div-exp
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
5×pow1 pow-exp
4×add-log-exp
3×times-frac associate-*r* sqrt-prod 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--
Counts
4 → 88
Calls
4 calls:
15.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
48.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
23.0ms
(/ (* M D) (* 2.0 d))
23.0ms
(/ (* M D) (* 2.0 d))

series1.7s

Counts
4 → 12
Calls
4 calls:
593.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
50.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(/ (* M D) (* 2.0 d))

simplify937.0ms

Counts
100 → 100

prune569.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.5b

localize27.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))
4.9b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))))
6.7b
(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
7.4b
(/ (* M D) (* 2.0 d))

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
1390×add-exp-log
903×prod-exp
362×div-exp
305×pow-exp
61×pow-to-exp
57×rec-exp 1-exp
39×add-cbrt-cube
18×add-sqr-sqrt
17×cbrt-unprod
16×associate-*r*
14×add-cube-cbrt *-un-lft-identity
10×times-frac
7×pow1 cbrt-undiv
6×associate-*l*
4×add-log-exp
3×sqrt-prod
2×sqrt-div *-commutative div-inv unswap-sqr sqr-pow
1×unpow-prod-down rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 321
Calls
4 calls:
126.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))
10.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))))
27.0ms
(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
19.0ms
(/ (* M D) (* 2.0 d))

series2.6s

Counts
4 → 12
Calls
4 calls:
949.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))
600.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))))
997.0ms
(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
53.0ms
(/ (* M D) (* 2.0 d))

simplify2.0s

Counts
333 → 333

prune624.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.5b

regimes1.1s

Accuracy

0% (1.7b remaining)

Error of 9.5b against oracle of 7.8b and baseline of 9.5b

bsearch0.0ms

simplify1.3s

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.5s9368×body80valid
402.0ms3151×body80nan