Details

Time bar (total: 1.5m)

sample862.0ms

Algorithm
intervals
Results
539.0ms1347×body80nan
226.0ms403×body80valid

simplify5.3s

Counts
1 → 1
Iterations
IterNodes
49030
31081
2188
155
022

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.5b

localize106.0ms

Local error

Found 4 expressions with local error:

7.0b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
12.6b
(pow (/ d h) (/ 1 2))
13.3b
(pow (/ d l) (/ 1 2))
14.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
331×add-exp-log
179×prod-exp
99×div-exp
60×pow-exp
45×times-frac
40×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×insert-posit16 add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 208
Calls
4 calls:
72.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
8.0ms
(pow (/ d h) (/ 1 2))
5.0ms
(pow (/ d l) (/ 1 2))
70.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series678.0ms

Counts
4 → 12
Calls
4 calls:
380.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
94.0ms
(pow (/ d h) (/ 1 2))
96.0ms
(pow (/ d l) (/ 1 2))
108.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify8.4s

Counts
220 → 220
Iterations
IterNodes
24118
11283
0438

prune4.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 14.3b

localize152.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* M D) (* 2 d))
7.0b
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
13.3b
(pow (/ d l) (/ 1 2))
14.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite986.0ms

Algorithm
rewrite-expression-head
Rules
320×add-exp-log
171×prod-exp
96×div-exp
46×add-cbrt-cube associate-*l/ pow-exp
30×frac-times sqrt-div
28×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow unpow-prod-down
12×associate-*r/
11×pow-to-exp
9×pow1 cbrt-undiv
8×flip3-- flip--
4×insert-posit16 div-inv add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 205
Calls
4 calls:
13.0ms
(/ (* M D) (* 2 d))
878.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.0ms
(pow (/ d l) (/ 1 2))
83.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series620.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2 d))
381.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
87.0ms
(pow (/ d l) (/ 1 2))
117.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify5.1s

Counts
217 → 217
Iterations
IterNodes
25164
11395
0468

prune5.3s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 12.8b

localize120.0ms

Local error

Found 4 expressions with local error:

6.4b
(* h (/ (/ M (/ d D)) 2))
6.8b
(/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))
7.0b
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))))
13.3b
(pow (/ d l) (/ 1 2))

rewrite942.0ms

Algorithm
rewrite-expression-head
Rules
355×times-frac
336×add-exp-log
312×add-cbrt-cube
187×add-sqr-sqrt
173×*-un-lft-identity
170×add-cube-cbrt
159×div-exp
156×cbrt-undiv
142×associate-*r*
118×prod-exp
103×cbrt-unprod
44×associate-*l/
30×frac-times sqrt-div
16×div-inv
15×associate-*r/
13×pow-unpow unpow-prod-down
9×pow1
8×flip3-- flip--
6×pow-exp
4×associate-*l* insert-posit16 add-log-exp unswap-sqr
3×pow-to-exp associate-/r/ associate-/l/
2×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down *-commutative difference-of-squares
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* distribute-lft-out-- sqr-pow
Counts
4 → 358
Calls
4 calls:
35.0ms
(* h (/ (/ M (/ d D)) 2))
98.0ms
(/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))
777.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))))
10.0ms
(pow (/ d l) (/ 1 2))

series717.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* h (/ (/ M (/ d D)) 2))
175.0ms
(/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))
381.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))))
105.0ms
(pow (/ d l) (/ 1 2))

simplify2.3s

Counts
370 → 370
Iterations
IterNodes
12633
0815

prune9.6s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 8.6b

localize167.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ M (/ d D))
6.4b
(* h (/ (/ M (/ d D)) 2))
6.8b
(/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))
7.0b
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) 1/2))) (- 1 (/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
625×add-exp-log
412×times-frac
331×prod-exp
326×add-cbrt-cube
215×add-sqr-sqrt
205×div-exp
201×*-un-lft-identity
198×add-cube-cbrt
159×cbrt-undiv
142×associate-*r*
110×cbrt-unprod
68×pow-exp
44×associate-*l/
30×frac-times sqrt-div
22×pow-to-exp
19×div-inv
15×pow1 associate-*r/
14×associate-/r*
8×flip3-- flip--
7×pow-prod-down
4×associate-*l* associate-/r/ insert-posit16 associate-/l* add-log-exp unswap-sqr
3×associate-/l/
2×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in *-commutative difference-of-squares
1×distribute-lft-out--
Counts
4 → 444
Calls
4 calls:
12.0ms
(/ M (/ d D))
31.0ms
(* h (/ (/ M (/ d D)) 2))
85.0ms
(/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))
1.4s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) 1/2))) (- 1 (/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))))

series679.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ M (/ d D))
60.0ms
(* h (/ (/ M (/ d D)) 2))
180.0ms
(/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))
400.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) 1/2))) (- 1 (/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))))

simplify2.0s

Counts
456 → 456
Iterations
IterNodes
12753
0895

prune13.2s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 8.3b

regimes3.3s

Accuracy

0% (4.4b remaining)

Error of 11.7b against oracle of 7.4b and baseline of 11.7b

bsearch0.0ms

simplify14.0ms

Iterations
IterNodes
237
137
031

end0.0ms

sample24.3s

Algorithm
intervals
Results
15.9s38235×body80nan
5.4s12653×body80valid