Details

Time bar (total: 7.5m)

sample731.0ms

Algorithm
intervals
Results
446.0ms1202×body80nan
216.0ms392×body80valid

simplify406.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
406.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.3b

localize73.0ms

Local error

Found 4 expressions with local error:

13.3b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.5b
(pow (/ d l) (/ 1 2))
12.4b
(pow (/ d h) (/ 1 2))
5.5b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite137.0ms

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
65.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
45.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.0ms
(pow (/ d h) (/ 1 2))
9.0ms
(pow (/ d l) (/ 1 2))

series689.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
388.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
109.0ms
(pow (/ d h) (/ 1 2))
97.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
94.0ms
(pow (/ d l) (/ 1 2))

simplify40.6s

Counts
182 → 220
Calls
182 calls:
Slowest
905.0ms
(* (* (* (* (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)))))
905.0ms
(* (* (* (* (/ 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)))
861.0ms
(+ (+ (- 0 (log 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (log (/ h l)))
813.0ms
(* (* (* (* (/ 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)))
698.0ms
(+ (+ (* (log (/ d h)) (/ 1 2)) (log (pow (/ d l) (/ 1 2)))) (log (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))

prune4.3s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 10.2b

localize91.0ms

Local error

Found 4 expressions with local error:

13.3b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.5b
(pow (/ d l) (/ 1 2))
5.5b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.4b
(/ (* M D) (* 2 d))

rewrite272.0ms

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
163.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
76.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
21.0ms
(/ (* M D) (* 2 d))
4.0ms
(pow (/ d l) (/ 1 2))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
142.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
109.0ms
(pow (/ d l) (/ 1 2))
49.0ms
(/ (* M D) (* 2 d))

simplify45.9s

Counts
168 → 208
Calls
168 calls:
Slowest
1.1s
(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt 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)))))
1.1s
(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))) (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt 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)))))
947.0ms
(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))) (fabs (/ (cbrt d) (cbrt h)))) (* (* (pow (/ (cbrt d) (cbrt h)) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ (cbrt d) (cbrt 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)))))
939.0ms
(* (* (* (* (/ 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)))
742.0ms
(* (* (* (* (/ 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)))

prune5.0s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 8.3b

localize115.0ms

Local error

Found 4 expressions with local error:

12.5b
(pow (/ d l) (/ 1 2))
7.1b
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
5.5b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))
5.4b
(/ (* M D) (* 2 d))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
1979×add-exp-log
1199×prod-exp
692×div-exp
220×pow-exp
186×1-exp
107×add-cbrt-cube
70×rec-exp
66×cbrt-unprod
50×pow-to-exp
37×times-frac
32×add-sqr-sqrt cbrt-undiv *-un-lft-identity add-cube-cbrt
25×associate-*r*
13×pow-unpow unpow-prod-down
12×pow1
9×cbrt-prod associate-*l/
5×frac-times associate-*r/
4×pow-prod-down insert-posit16 div-inv add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 458
Calls
4 calls:
Slowest
209.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
138.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))
21.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ d l) (/ 1 2))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))
180.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
103.0ms
(pow (/ d l) (/ 1 2))
38.0ms
(/ (* M D) (* 2 d))

simplify2.1m

Counts
432 → 470
Calls
432 calls:
Slowest
1.4s
(* (* (* (/ (* (* 1 1) 1) (* (* 2 2) 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ (* (cbrt h) (cbrt h)) 1) (/ (* (cbrt h) (cbrt h)) 1)) (/ (* (cbrt h) (cbrt h)) 1))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))
1.4s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))) (/ h (* (* l l) 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))) (* (* (/ (* (cbrt h) (cbrt h)) 1) (/ (* (cbrt h) (cbrt h)) 1)) (/ (* (cbrt h) (cbrt h)) 1))) (/ h (* (* l l) l)))
1.2s
(+ (+ (+ (log (/ 1 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (- (log (* (cbrt h) (cbrt h))) (log 1))) (log (/ (cbrt h) l)))
1.2s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))

prune12.2s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 6.7b

localize115.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
5.5b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (pow (/ d (cbrt l)) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))
5.4b
(/ (* M D) (* 2 d))
3.9b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))

rewrite929.0ms

Algorithm
rewrite-expression-head
Rules
2736×add-exp-log
1656×prod-exp
958×div-exp
320×pow-exp
279×1-exp
146×add-cbrt-cube
105×rec-exp
91×cbrt-unprod
70×pow-to-exp
41×cbrt-undiv
32×associate-*r*
22×times-frac
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×pow1 associate-*l/
9×cbrt-prod associate-*r/
8×frac-times
7×pow-prod-down
4×insert-posit16 add-log-exp
3×sqrt-div associate-*l* *-commutative div-inv
2×distribute-rgt-in sub-neg distribute-lft-in flip3-- flip--
1×clear-num associate-/r* frac-2neg associate-/l*
Counts
4 → 605
Calls
4 calls:
Slowest
627.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (pow (/ d (cbrt l)) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))
201.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
60.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))
11.0ms
(/ (* M D) (* 2 d))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (pow (/ d (cbrt l)) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))
249.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))
165.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
38.0ms
(/ (* M D) (* 2 d))

simplify3.0m

Counts
582 → 617
Calls
582 calls:
Slowest
1.4s
(* (* (* (/ (* (* 1 1) 1) (* (* 2 2) 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ (* (cbrt h) (cbrt h)) 1) (/ (* (cbrt h) (cbrt h)) 1)) (/ (* (cbrt h) (cbrt h)) 1))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))
1.3s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))) (/ h (* (* l l) l)))
1.3s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt 1) (pow (/ d (cbrt l)) (/ 1 2)))) (- (pow 1 3) (pow (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)) 3)))
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))) (* (* (/ (* (cbrt h) (cbrt h)) 1) (/ (* (cbrt h) (cbrt h)) 1)) (/ (* (cbrt h) (cbrt h)) 1))) (/ h (* (* l l) l)))
1.2s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))

prune13.6s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 5.9b

regimes1.9s

Accuracy

17.5% (5.5b remaining)

Error of 13.0b against oracle of 7.5b and baseline of 14.2b

bsearch28.0ms

end0.0ms

sample15.5s

Algorithm
intervals
Results
10.5s38581×body80nan
3.7s12882×body80valid