Details

Time bar (total: 7.4m)

sample732.0ms

Algorithm
intervals
Results
408.0ms1139×body80nan
199.0ms389×body80valid

simplify434.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
433.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.3b

localize106.0ms

Local error

Found 4 expressions with local error:

14.0b
(pow (/ d l) (/ 1 2))
11.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.3b
(pow (/ d h) (/ 1 2))
5.9b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite155.0ms

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
75.0ms
(* (* (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 l) (/ 1 2))
9.0ms
(pow (/ d h) (/ 1 2))

series686.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
366.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
110.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
108.0ms
(pow (/ d h) (/ 1 2))
101.0ms
(pow (/ d l) (/ 1 2))

simplify41.6s

Counts
182 → 220
Calls
182 calls:
Slowest
1.0s
(* (* (* (* (/ 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)))
924.0ms
(+ (+ (- (log 1) (log 2)) (* (- (log (* M D)) (+ (log 2) (log d))) 2)) (- (log h) (log l)))
862.0ms
(* (* (* (* (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)))))
832.0ms
(* (* (* (* (/ 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)))
724.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (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)))))

prune4.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.3b

localize109.0ms

Local error

Found 4 expressions with local error:

11.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.3b
(pow (/ d h) (/ 1 2))
5.9b
(* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
3.5b
(/ (* M D) (* 2 d))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
368×add-exp-log
207×prod-exp
103×div-exp
60×pow-exp
46×add-cbrt-cube
28×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×cbrt-unprod
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow unpow-prod-down
9×pow1 cbrt-undiv
4×insert-posit16 div-inv add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 196
Calls
4 calls:
Slowest
136.0ms
(* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt 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))
13.0ms
(pow (/ d h) (/ 1 2))
12.0ms
(/ (* M D) (* 2 d))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
857.0ms
(* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
111.0ms
(pow (/ d h) (/ 1 2))
109.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
30.0ms
(/ (* M D) (* 2 d))

simplify46.8s

Counts
168 → 208
Calls
168 calls:
Slowest
1.2s
(* (* (* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2))))) (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt 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)))))
1.2s
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (* (fabs (/ (cbrt d) (cbrt l))) (fabs (/ (cbrt d) (cbrt l)))) (fabs (/ (cbrt d) (cbrt l)))) (* (* (pow (/ (cbrt d) (cbrt l)) (/ 1 2)) (pow (/ (cbrt d) (cbrt l)) (/ 1 2))) (pow (/ (cbrt d) (cbrt 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)))))
1.2s
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt 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)))))
1.0s
(* (* (/ (* (* 1 1) 1) (* (* 2 2) 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))
991.0ms
(* (* (* (* (/ 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)))

prune5.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.2b

localize125.0ms

Local error

Found 4 expressions with local error:

11.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.9b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
3.5b
(/ (* M D) (* 2 d))
0.6b
(cbrt l)

rewrite291.0ms

Algorithm
rewrite-expression-head
Rules
404×add-exp-log
241×prod-exp
103×div-exp
60×pow-exp
55×add-cbrt-cube
27×cbrt-unprod
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×pow1
10×times-frac
9×cbrt-undiv
4×pow-prod-down insert-posit16 add-log-exp
3×cbrt-prod associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative div-inv
1×frac-times clear-num associate-/r* frac-2neg flip3-- pow1/3 flip-- associate-/l*
Counts
4 → 177
Calls
4 calls:
Slowest
220.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
55.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.0ms
(/ (* M D) (* 2 d))
1.0ms
(cbrt l)

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
303.0ms
(cbrt l)
116.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
42.0ms
(/ (* M D) (* 2 d))

simplify47.9s

Counts
150 → 189
Calls
150 calls:
Slowest
857.0ms
(* (* (* (* (/ 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)))
800.0ms
(* (* (* (* (/ 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)))
731.0ms
(* (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))))
722.0ms
(- (* (* (fabs (pow (/ d l) 1/3)) (* (fabs (pow (/ d h) 1/3)) (exp (* 1/6 (+ (log (/ 1 h)) (log (/ 1 l))))))) (pow d 1/3)) (* 1/8 (* (* (exp (* 1/6 (- (* 7 (log (/ 1 l))) (* 5 (log (/ 1 h)))))) (* (pow M 2) (* (fabs (pow (/ d h) 1/3)) (* (pow D 2) (fabs (pow (/ d l) 1/3)))))) (pow (/ 1 (pow d 5)) 1/3))))
711.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune5.5s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 6.9b

localize152.0ms

Local error

Found 4 expressions with local error:

5.9b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
5.4b
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
5.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l))))
3.5b
(/ (* M D) (* 2 d))

rewrite604.0ms

Algorithm
rewrite-expression-head
Rules
3723×add-exp-log
2297×prod-exp
1196×div-exp
440×pow-exp
321×rec-exp 1-exp
146×add-cbrt-cube
94×pow-to-exp
91×cbrt-unprod
41×cbrt-undiv
32×associate-*r*
22×times-frac
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×pow1
13×associate-*l/
9×cbrt-prod
7×frac-times pow-prod-down
6×associate-*r/
4×insert-posit16 add-log-exp
3×associate-*l* un-div-inv *-commutative div-inv
2×distribute-rgt-in sub-neg distribute-lft-in
1×clear-num associate-/r* frac-2neg flip3-- flip-- associate-/l*
Counts
4 → 779
Calls
4 calls:
Slowest
229.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
207.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
102.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l))))
11.0ms
(/ (* M D) (* 2 d))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
260.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l))))
207.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
29.0ms
(/ (* M D) (* 2 d))

simplify3.8m

Counts
757 → 791
Calls
757 calls:
Slowest
1.4s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* 1 1) 1) (* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (* (cbrt l) (cbrt l))))) (* (* (/ h (cbrt l)) (/ h (cbrt l))) (/ h (cbrt l))))
1.4s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
1.4s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ 1 (* (cbrt l) (cbrt l))) (/ 1 (* (cbrt l) (cbrt l)))) (/ 1 (* (cbrt l) (cbrt l))))) (* (* (/ h (cbrt l)) (/ h (cbrt l))) (/ h (cbrt l))))
1.3s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* 1 1) 1) (* l l))) (* (* (/ h (cbrt l)) (/ h (cbrt l))) (/ h (cbrt l))))
1.2s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ 1 (* (cbrt l) (cbrt l))) (/ 1 (* (cbrt l) (cbrt l)))) (/ 1 (* (cbrt l) (cbrt l))))) (/ (* (* h h) h) l))

prune24.7s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 4.4b

regimes2.8s

Accuracy

0% (4.1b remaining)

Error of 10.4b against oracle of 6.3b and baseline of 10.4b

bsearch12.0ms

end0.0ms

sample25.2s

Algorithm
intervals
Results
16.6s38369×body80nan
5.8s12705×body80valid