Details

Time bar (total: 1.2m)

sample768.0ms

Algorithm
intervals
Results
470.0ms1199×body80nan
188.0ms388×body80valid

simplify5.3s

Counts
1 → 1

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.7b

localize103.0ms

Local error

Found 4 expressions with local error:

15.4b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.3b
(pow (/ d l) (/ 1 2))
10.6b
(pow (/ d h) (/ 1 2))
6.3b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
331×add-exp-log
179×prod-exp
99×div-exp
60×pow-exp
45×times-frac
42×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
6×prod-diff
5×distribute-rgt-in cbrt-undiv distribute-lft-in div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 222
Calls
4 calls:
Slowest
67.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
51.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.0ms
(pow (/ d h) (/ 1 2))
9.0ms
(pow (/ d l) (/ 1 2))

series707.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
416.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
108.0ms
(pow (/ d l) (/ 1 2))
101.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
83.0ms
(pow (/ d h) (/ 1 2))

simplify1.8s

Counts
234 → 234

prune4.2s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 10.9b

localize109.0ms

Local error

Found 4 expressions with local error:

11.3b
(pow (/ d l) (/ 1 2))
10.6b
(pow (/ d h) (/ 1 2))
7.2b
(/ D (/ (* d 2) M))
7.2b
(/ D (/ (* d 2) M))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
64×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
28×add-exp-log
26×pow-unpow unpow-prod-down
22×add-cbrt-cube
14×associate-/r* div-inv
12×div-exp
10×cbrt-undiv
6×pow1 associate-/l*
4×expm1-log1p-u pow-exp insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp clear-num pow-pow frac-2neg prod-exp associate-/r/ cbrt-unprod sqr-pow
Counts
4 → 184
Calls
4 calls:
Slowest
10.0ms
(pow (/ d h) (/ 1 2))
10.0ms
(/ D (/ (* d 2) M))
9.0ms
(/ D (/ (* d 2) M))
5.0ms
(pow (/ d l) (/ 1 2))

series262.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(pow (/ d l) (/ 1 2))
85.0ms
(pow (/ d h) (/ 1 2))
39.0ms
(/ D (/ (* d 2) M))
39.0ms
(/ D (/ (* d 2) M))

simplify1.4s

Counts
196 → 196

prune4.3s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 7.4b

localize138.0ms

Local error

Found 4 expressions with local error:

10.6b
(pow (/ d h) (/ 1 2))
7.2b
(/ D (/ (* d 2) M))
7.2b
(/ D (/ (* d 2) M))
6.3b
(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (/ (* (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l))) (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l)))) 2) (/ (cbrt h) (cbrt l)))))

rewrite610.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
55×add-exp-log
53×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
32×associate-*r/
31×add-cbrt-cube
30×sqrt-div
29×frac-times
23×prod-exp
22×associate-*l/
14×associate-/r*
13×pow-unpow unpow-prod-down div-exp
12×div-inv
10×cbrt-undiv
8×flip3-- cbrt-unprod flip--
7×pow1
6×prod-diff pow-exp associate-/l*
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp associate-*r*
2×clear-num sub-neg frac-2neg associate-/r/
1×pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
Counts
4 → 204
Calls
4 calls:
Slowest
581.0ms
(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (/ (* (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l))) (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l)))) 2) (/ (cbrt h) (cbrt l)))))
9.0ms
(pow (/ d h) (/ 1 2))
7.0ms
(/ D (/ (* d 2) M))
7.0ms
(/ D (/ (* d 2) M))

series577.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
409.0ms
(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (/ (* (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l))) (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l)))) 2) (/ (cbrt h) (cbrt l)))))
95.0ms
(pow (/ d h) (/ 1 2))
39.0ms
(/ D (/ (* d 2) M))
34.0ms
(/ D (/ (* d 2) M))

simplify2.6s

Counts
216 → 216

prune5.7s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 6.3b

localize133.0ms

Local error

Found 4 expressions with local error:

7.2b
(/ D (/ (* d 2) M))
7.2b
(/ D (/ (* d 2) M))
6.3b
(* (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) h))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (/ (* (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l))) (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l)))) 2) (/ (cbrt h) (cbrt l)))))
2.5b
(* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l)))

rewrite710.0ms

Algorithm
rewrite-expression-head
Rules
145×times-frac
111×add-sqr-sqrt
84×sqrt-div
82×frac-times
78×*-un-lft-identity add-cube-cbrt
72×add-exp-log
66×associate-*r/
64×add-cbrt-cube
49×associate-*l/
44×cbrt-prod
43×associate-*r*
27×associate-*l*
25×prod-exp cbrt-unprod
24×pow1 cbrt-undiv div-exp
16×flip3-- flip--
15×div-inv
14×associate-/r* pow-prod-down
10×unswap-sqr
6×prod-diff associate-/l*
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r/
2×clear-num sub-neg frac-2neg *-commutative
Counts
4 → 296
Calls
4 calls:
Slowest
630.0ms
(* (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) h))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (/ (* (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l))) (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l)))) 2) (/ (cbrt h) (cbrt l)))))
47.0ms
(* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l)))
17.0ms
(/ D (/ (* d 2) M))
8.0ms
(/ D (/ (* d 2) M))

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
2.0s
(* (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) h))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (/ (* (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l))) (* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l)))) 2) (/ (cbrt h) (cbrt l)))))
182.0ms
(* (/ D (/ (* d 2) M)) (/ (cbrt h) (cbrt l)))
46.0ms
(/ D (/ (* d 2) M))
31.0ms
(/ D (/ (* d 2) M))

simplify2.0s

Counts
308 → 308

prune9.2s

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 5.9b

regimes2.8s

Accuracy

9.8% (4.8b remaining)

Error of 11.3b against oracle of 6.6b and baseline of 11.9b

bsearch1.0s

end0.0ms

sample23.6s

Algorithm
intervals
Results
15.1s37335×body80nan
5.6s12716×body80valid