Details

Time bar (total: 4.7m)

sample755.0ms

Algorithm
intervals
Results
485.0ms1344×body80nan
151.0ms414×body80valid

simplify367.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
367.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.4b

localize101.0ms

Local error

Found 4 expressions with local error:

12.5b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.1b
(pow (/ d l) (/ 1 2))
9.3b
(pow (/ d h) (/ 1 2))
6.2b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite134.0ms

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
69.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
48.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
7.0ms
(pow (/ d h) (/ 1 2))
5.0ms
(pow (/ d l) (/ 1 2))

series633.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
365.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
106.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
95.0ms
(pow (/ d h) (/ 1 2))
67.0ms
(pow (/ d l) (/ 1 2))

simplify41.2s

Counts
182 → 220
Calls
182 calls:
Slowest
915.0ms
(* (* (* (* (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)))))
849.0ms
(* (* (* (* (/ 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)))
787.0ms
(+ (+ (- (log 1) (log 2)) (* (log (/ (* M D) (* 2 d))) 2)) (- (log h) (log l)))
776.0ms
(* (* (* (* (/ 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)))
774.0ms
(* (* (* (* (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

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.5b

localize116.0ms

Local error

Found 4 expressions with local error:

12.5b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.1b
(pow (/ d l) (/ 1 2))
6.2b
(* (* (* (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))))
3.8b
(/ (* M D) (* 2 d))

rewrite239.0ms

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
150.0ms
(* (* (* (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))))
56.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
15.0ms
(/ (* M D) (* 2 d))
9.0ms
(pow (/ d l) (/ 1 2))

series1.6s

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))))
123.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
86.0ms
(pow (/ d l) (/ 1 2))
45.0ms
(/ (* M D) (* 2 d))

simplify46.4s

Counts
168 → 208
Calls
168 calls:
Slowest
1.2s
(* (* (* (* (* (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)))))
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)))))
1.1s
(* (* (/ (* (* 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)))
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)))))
1.0s
(* (* (* (* (/ 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)))

prune4.9s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 9.7b

localize106.0ms

Local error

Found 4 expressions with local error:

12.5b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.2b
(* (* (* (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))))
3.8b
(/ (* M D) (* 2 d))
0.6b
(cbrt h)

rewrite319.0ms

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
224.0ms
(* (* (* (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))))
62.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
23.0ms
(/ (* M D) (* 2 d))
1.0ms
(cbrt h)

series2.0s

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))))
256.0ms
(cbrt h)
148.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
41.0ms
(/ (* M D) (* 2 d))

simplify47.1s

Counts
150 → 189
Calls
150 calls:
Slowest
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)))
843.0ms
(* (* (* (* (/ 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)))
784.0ms
(* (* (* (* (/ 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)))
758.0ms
(* (- (* (* (/ 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)))))
727.0ms
(+ (+ (- (log 1) (log 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (- (log h) (log l)))

prune5.2s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 6.8b

localize125.0ms

Local error

Found 4 expressions with local error:

6.9b
(* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)
6.2b
(* (* (* (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 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
5.8b
(/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))
3.8b
(/ (* D M) (* 2 d))

rewrite650.0ms

Algorithm
rewrite-expression-head
Rules
687×add-exp-log
588×add-cbrt-cube
395×prod-exp
317×cbrt-unprod
188×div-exp
178×cbrt-undiv
20×pow-exp
14×pow1
10×add-sqr-sqrt pow-to-exp
9×*-un-lft-identity associate-*r*
8×associate-*l/
6×pow-prod-down add-cube-cbrt
4×associate-*r/ insert-posit16 add-log-exp
3×associate-/l/
2×distribute-rgt-in frac-times clear-num associate-/r* sub-neg frac-2neg distribute-lft-in times-frac associate-*l* *-commutative div-inv associate-/l* difference-of-squares
1×flip3-- flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 273
Calls
4 calls:
Slowest
265.0ms
(* (* (* (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 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
194.0ms
(/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))
154.0ms
(* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)
16.0ms
(/ (* D M) (* 2 d))

series1.8s

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 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
121.0ms
(/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))
118.0ms
(* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)
51.0ms
(/ (* D M) (* 2 d))

simplify1.4m

Counts
244 → 285
Calls
244 calls:
Slowest
2.5s
(/ (* (* (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
2.5s
(* (* (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
2.4s
(/ (* (* (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) (/ (* D M) (* 2 d))) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) (/ (* D M) (* 2 d)))) (* (* h h) h)) (* (* (* 2 2) 2) (* (* l l) l)))
2.3s
(* (* (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* h h) h))
2.1s
(* (* (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))

prune7.8s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 4.6b

regimes4.0s

Accuracy

35% (3.5b remaining)

Error of 9.8b against oracle of 6.3b and baseline of 11.7b

bsearch1.3s

end0.0ms

sample24.4s

Algorithm
intervals
Results
15.1s38870×body80nan
6.3s12722×body80valid