Details

Time bar (total: 5.5m)

sample740.0ms

Algorithm
intervals
Results
445.0ms1183×body80nan
171.0ms421×body80valid

simplify303.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
302.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.4b

localize71.0ms

Local error

Found 4 expressions with local error:

11.9b
(pow (/ d h) (/ 1 2))
11.9b
(pow (/ d l) (/ 1 2))
10.4b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.1b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite163.0ms

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:
Slowest
74.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
72.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.0ms
(pow (/ d h) (/ 1 2))
4.0ms
(pow (/ d l) (/ 1 2))

series675.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
373.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
140.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
83.0ms
(pow (/ d h) (/ 1 2))
79.0ms
(pow (/ d l) (/ 1 2))

simplify1.0m

Counts
251 → 220
Calls
251 calls:
Slowest
929.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- (pow 1 3) (pow (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) 3)))
886.0ms
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))
879.0ms
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))
859.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
857.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))) (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))

prune4.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 10.0b

localize88.0ms

Local error

Found 4 expressions with local error:

11.9b
(pow (/ d l) (/ 1 2))
10.4b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.1b
(* (* (* (fabs (/ (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))))
4.4b
(/ (* M D) (* 2 d))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
320×add-exp-log
171×prod-exp
96×div-exp
46×add-cbrt-cube pow-exp
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
11×pow-to-exp
9×pow1 cbrt-undiv
7×associate-*l/
6×associate-*r/
4×insert-posit16 div-inv add-log-exp
3×frac-times sqrt-div
2×distribute-rgt-in sub-neg distribute-lft-in flip3-- associate-*l* pow-prod-down *-commutative flip--
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 187
Calls
4 calls:
Slowest
207.0ms
(* (* (* (fabs (/ (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))))
49.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
21.0ms
(/ (* M D) (* 2 d))
20.0ms
(pow (/ d l) (/ 1 2))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(* (* (* (fabs (/ (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))))
123.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
111.0ms
(pow (/ d l) (/ 1 2))
47.0ms
(/ (* M D) (* 2 d))

simplify1.0m

Counts
220 → 199
Calls
220 calls:
Slowest
1.3s
(* (* (* (* (* (fabs (/ (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)))) (* (* (* (fabs (/ (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))))) (* (* (* (fabs (/ (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)))))
1.1s
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))
1.0s
(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))) (fabs (/ (cbrt d) (cbrt h)))) (* (* (sqrt (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h))))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
999.0ms
(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2)))) (* (* (fabs (/ (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))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
970.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (cbrt d))) (pow (/ d l) (/ 1 2))) (- (pow 1 3) (pow (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) 3)))

prune4.7s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 8.0b

localize127.0ms

Local error

Found 4 expressions with local error:

11.9b
(pow (/ d l) (/ 1 2))
8.1b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))))
5.0b
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
5.0b
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
119×add-exp-log
79×add-cbrt-cube
57×prod-exp
42×cbrt-unprod
36×times-frac
33×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
29×div-exp
27×associate-*l*
26×cbrt-undiv
17×pow1
15×associate-*r/
13×pow-unpow unpow-prod-down
12×frac-times
10×associate-*l/
7×pow-prod-down
6×pow-exp
5×associate-*r*
4×insert-posit16 div-inv add-log-exp
3×pow-to-exp sqrt-div *-commutative
2×distribute-rgt-in sub-neg distribute-lft-in flip3-- flip--
1×pow-pow sqr-pow
Counts
4 → 178
Calls
4 calls:
Slowest
207.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))))
55.0ms
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
54.0ms
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
10.0ms
(pow (/ d l) (/ 1 2))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))))
172.0ms
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
160.0ms
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
109.0ms
(pow (/ d l) (/ 1 2))

simplify1.1m

Counts
213 → 190
Calls
213 calls:
Slowest
1.2s
(* (sqrt (cbrt h)) (+ (* 1 1) (+ (* (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))) (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))) (* 1 (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))))))
1.2s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- (pow 1 3) (pow (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))) 3)))
1.1s
(sqrt (* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))))))
1.1s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (cbrt d))) (pow (/ d l) (/ 1 2))) (- (pow 1 3) (pow (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))) 3)))
1.0s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- (* 1 1) (* (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))) (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))))))

prune5.0s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 6.9b

localize145.0ms

Local error

Found 4 expressions with local error:

8.1b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))))
5.0b
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
5.0b
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
2.2b
(* (/ D d) (/ (cbrt h) (cbrt l)))

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
116×add-exp-log
96×add-cbrt-cube
84×add-sqr-sqrt
76×times-frac
53×prod-exp cbrt-unprod
51×*-un-lft-identity add-cube-cbrt
45×associate-*r*
44×cbrt-prod
40×associate-*l*
34×pow1
30×cbrt-undiv div-exp
28×associate-*r/
20×frac-times pow-prod-down
13×associate-*l/
12×sqrt-div
10×unswap-sqr
4×flip3-- *-commutative insert-posit16 div-inv flip-- add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in
Counts
4 → 231
Calls
4 calls:
Slowest
237.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))))
54.0ms
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
30.0ms
(* (/ D d) (/ (cbrt h) (cbrt l)))
27.0ms
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.7s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))))
154.0ms
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
135.0ms
(* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))
74.0ms
(* (/ D d) (/ (cbrt h) (cbrt l)))

simplify1.4m

Counts
266 → 243
Calls
266 calls:
Slowest
1.3s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (cbrt d))) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (cbrt d)))) (- (* 1 1) (* (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))) (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))))))
1.3s
(* (- (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))) (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l))))))
1.2s
(* (sqrt (cbrt h)) (+ (* 1 1) (+ (* (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))) (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))) (* 1 (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l)))))))
1.2s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l))))) (- (pow 1 3) (pow (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))) 3)))
1.2s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (cbrt d))) (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (cbrt d)))) (- (pow 1 3) (pow (* (/ (* (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l)))) (* (/ M 2) (* (/ D d) (/ (cbrt h) (cbrt l))))) 2) (/ (cbrt h) (cbrt l))) 3)))

prune6.6s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 6.1b

regimes3.1s

Accuracy

0% (4.3b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 10.2b

bsearch11.0ms

end0.0ms

sample24.7s

Algorithm
intervals
Results
15.6s38146×body80nan
6.6s12695×body80valid