Details

Time bar (total: 58.6s)

sample104.0ms

Algorithm
intervals
Results
38.0ms307×body80valid
12.0ms97×body80nan

simplify21.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01718
16518
231218
3349118
done500118

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize18.0ms

Local error

Found 4 expressions with local error:

3.1b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.9b
(/ (* M D) (* 2.0 d))
13.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
25.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
20.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.6s

Counts
4 → 12
Calls
4 calls:
625.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
557.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
38.0ms
(/ (* M D) (* 2.0 d))
1.3s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify3.6s

Counts
125 → 125
Iterations

Useful iterations: done (3.6s)

IterNodesCost
02362311
137372083
done50001927

prune626.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.3b

localize75.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
4.4b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.9b
(/ (* M D) (* 2.0 d))
6.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite325.0ms

Algorithm
rewrite-expression-head
Rules
609×add-exp-log
325×prod-exp
184×div-exp
75×pow-exp
54×add-cbrt-cube
45×associate-*r*
43×cbrt-unprod
42×times-frac
41×add-sqr-sqrt
36×cbrt-prod
33×add-cube-cbrt *-un-lft-identity
22×cbrt-undiv
15×pow-to-exp
10×associate-*l*
7×pow1 unpow-prod-down
6×unswap-sqr
4×associate-*r/ div-inv add-log-exp
3×sqrt-prod sqr-pow
2×sqrt-div *-commutative
1×frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num associate-/r* flip-- associate-/l*
Counts
4 → 242
Calls
4 calls:
205.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
7.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
13.0ms
(/ (* M D) (* 2.0 d))
77.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.5s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
559.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
43.0ms
(/ (* M D) (* 2.0 d))
848.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify4.6s

Counts
254 → 254
Iterations

Useful iterations: done (4.6s)

IterNodesCost
04447867
done50017079

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize41.0ms

Local error

Found 4 expressions with local error:

4.4b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
4.9b
(/ (* M D) (* 2.0 d))
4.9b
(/ (* M D) (* 2.0 d))
6.1b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
189×add-exp-log
91×prod-exp
56×div-exp
38×add-cbrt-cube
25×pow-exp
17×cbrt-unprod
16×add-sqr-sqrt
12×cbrt-undiv
9×associate-*l*
8×add-cube-cbrt *-un-lft-identity
7×unpow-prod-down times-frac
6×unswap-sqr
5×pow1 pow-to-exp associate-*r*
4×div-inv add-log-exp
3×sqrt-prod sqr-pow
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 126
Calls
4 calls:
5.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
21.0ms
(/ (* M D) (* 2.0 d))
25.0ms
(/ (* M D) (* 2.0 d))
80.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series1.6s

Counts
4 → 12
Calls
4 calls:
613.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
34.0ms
(/ (* M D) (* 2.0 d))
51.0ms
(/ (* M D) (* 2.0 d))
859.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify4.0s

Counts
138 → 138
Iterations

Useful iterations: done (4.0s)

IterNodesCost
02503786
123583233
done50002569

prune733.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.0b

localize112.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
19.2b
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))))
19.2b
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))))
19.2b
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
83×prod-exp
48×div-exp
25×pow-exp
14×add-sqr-sqrt add-cbrt-cube
9×associate-*l* cbrt-unprod
7×add-cube-cbrt unpow-prod-down *-un-lft-identity
6×unswap-sqr
5×pow-to-exp times-frac associate-*r*
4×pow1 cbrt-undiv associate-*r/ add-log-exp
3×cbrt-prod cbrt-div pow1/3 sqr-pow
2×div-inv
1×*-commutative
Counts
4 → 99
Calls
4 calls:
109.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
38.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))))
55.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))))
53.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))))

series3.5s

Counts
4 → 12
Calls
4 calls:
883.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
873.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))))
923.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))))
855.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))))

simplify6.6s

Counts
111 → 111
Iterations

Useful iterations: done (6.6s)

IterNodesCost
02223406
117073181
done50012686

prune737.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.0b

regimes1.2s

Accuracy

27.1% (1.5b remaining)

Error of 9.1b against oracle of 7.6b and baseline of 9.6b

bsearch2.0ms

simplify19.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
045130
15799
done5799

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s9264×body80valid
337.0ms3005×body80nan