Details

Time bar (total: 1.1m)

sample634.0ms

Algorithm
intervals
Results
400.0ms1220×body80nan
158.0ms405×body80valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done2006
42006
31261
2198
158
022

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.8b

localize57.0ms

Local error

Found 4 expressions with local error:

7.5b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
11.6b
(pow (/ d h) (/ 1 2))
13.2b
(pow (/ d l) (/ 1 2))
13.5b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite133.0ms

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:
41.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
12.0ms
(pow (/ d h) (/ 1 2))
9.0ms
(pow (/ d l) (/ 1 2))
62.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series705.0ms

Counts
4 → 12
Calls
4 calls:
409.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
113.0ms
(pow (/ d h) (/ 1 2))
90.0ms
(pow (/ d l) (/ 1 2))
94.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.8s

Counts
220 → 220
Iterations
IterNodes
done2002
22002
11295
0438

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.6b

localize73.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (* M D) (* 2 d))
7.5b
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (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))))
13.2b
(pow (/ d l) (/ 1 2))
13.5b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite813.0ms

Algorithm
rewrite-expression-head
Rules
320×add-exp-log
171×prod-exp
96×div-exp
46×add-cbrt-cube associate-*l/ pow-exp
30×frac-times sqrt-div
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
12×associate-*r/
11×pow-to-exp
9×pow1 cbrt-undiv
8×flip3-- flip--
4×insert-posit16 div-inv add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 205
Calls
4 calls:
15.0ms
(/ (* M D) (* 2 d))
713.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (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))))
4.0ms
(pow (/ d l) (/ 1 2))
71.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series687.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (* M D) (* 2 d))
432.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (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))))
70.0ms
(pow (/ d l) (/ 1 2))
128.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.6s

Counts
217 → 217
Iterations
IterNodes
done2016
22016
11401
0468

prune1.6s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 10.7b

localize118.0ms

Local error

Found 4 expressions with local error:

2.4b
(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
3.5b
(/ (* M D) (* 2 d))
7.5b
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
13.5b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
515×frac-times
483×sqrt-div
328×associate-*l/
305×add-exp-log
169×associate-*r/
163×prod-exp
93×div-exp
64×flip3-- flip--
55×add-cbrt-cube
40×pow-exp
32×pow1
27×cbrt-unprod
16×associate-*r*
15×pow-prod-down
14×rec-exp 1-exp
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×times-frac
9×cbrt-undiv
8×pow-to-exp
6×sqrt-pow1
4×insert-posit16 add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative div-inv
1×pow2 rem-sqrt-square clear-num associate-/r* frac-2neg pow-plus pow1/2 pow-sqr pow-prod-up sqrt-prod associate-/l*
Counts
4 → 356
Calls
4 calls:
15.0ms
(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
23.0ms
(/ (* M D) (* 2 d))
1.2s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
73.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series645.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))))
38.0ms
(/ (* M D) (* 2 d))
369.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
126.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify1.8s

Counts
368 → 368
Iterations
IterNodes
done2000
12000
0705

prune4.5s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 8.5b

localize121.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (/ (* M D) 2) d)
6.3b
(* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)) (/ 1 l))
7.5b
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)) (/ 1 l))))
7.6b
(* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)

rewrite2.8s

Algorithm
rewrite-expression-head
Rules
2442×add-exp-log
1291×prod-exp
975×div-exp
746×add-cbrt-cube
531×frac-times
480×sqrt-div
365×cbrt-unprod
353×associate-*l/
278×cbrt-undiv
179×associate-*r/
145×rec-exp 1-exp
64×flip3-- flip--
42×times-frac
41×pow1
30×add-sqr-sqrt
29×*-un-lft-identity add-cube-cbrt
26×pow-prod-down
19×associate-*r*
7×associate-/l*
6×div-inv
4×insert-posit16 add-log-exp
3×associate-/r* associate-*l* *-commutative
2×distribute-rgt-in sub-neg distribute-lft-in
1×clear-num frac-2neg un-div-inv unswap-sqr associate-/l/
Counts
4 → 734
Calls
4 calls:
17.0ms
(/ (/ (* M D) 2) d)
1.3s
(* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)) (/ 1 l))
1.2s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)) (/ 1 l))))
121.0ms
(* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)

series697.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (/ (* M D) 2) d)
152.0ms
(* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)) (/ 1 l))
372.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* (/ 1 2) (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)) (/ 1 l))))
121.0ms
(* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h)

simplify11.1s

Counts
746 → 746
Iterations
IterNodes
done2000
12000
01235

prune5.5s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 8.3b

regimes2.6s

Accuracy

32.2% (3.5b remaining)

Error of 11.3b against oracle of 7.8b and baseline of 13.0b

bsearch4.0ms

simplify46.0ms

Iterations
IterNodes
done106
1106
078

end0.0ms

sample23.8s

Algorithm
intervals
Results
15.5s39069×body80nan
5.7s12798×body80valid