Details

Time bar (total: 37.6s)

sample55.0ms

Algorithm
intervals
Results
19.0ms298×body80valid
5.0ms75×body80nan

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5001
52702
4460
3181
281
136
017

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize30.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)) w0)
4.0b
(sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0))
5.1b
(fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)
7.0b
(/ (* M D) (* 2.0 d))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
13×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1 sqrt-prod
6×associate-*l*
5×prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
3×associate-*r*
2×unswap-sqr
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 times-frac pow1/2 pow-prod-down *-commutative fma-udef div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
8.0ms
(* (sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)) w0)
1.0ms
(sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0))
0.0ms
(fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)
10.0ms
(/ (* M D) (* 2.0 d))

series1.8s

Counts
4 → 12
Calls
4 calls:
849.0ms
(* (sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)) w0)
447.0ms
(sqrt (fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0))
460.0ms
(fma (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (- h) l) 1.0)
59.0ms
(/ (* M D) (* 2.0 d))

simplify1.3s

Counts
84 → 84
Iterations
IterNodes
done5000
21813
1416
0176

prune655.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.0b

localize50.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0)) w0)
4.0b
(sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0))
7.0b
(/ (* M D) (* 2.0 d))
8.9b
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
651×times-frac
304×add-sqr-sqrt
282×*-un-lft-identity
278×add-cube-cbrt
177×unpow-prod-down
90×distribute-lft-neg-in distribute-rgt-neg-in
67×add-exp-log
47×div-inv
37×sqr-pow
35×associate-/r*
33×div-exp
30×neg-mul-1
23×add-cbrt-cube
13×prod-exp
10×pow-exp associate-/l*
9×sqrt-prod
7×pow1 cbrt-undiv associate-*l* hypot-def
5×cbrt-unprod
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r*
2×pow-to-exp clear-num frac-2neg flip3-+ associate-*l/ flip-+ distribute-lft-out unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-/r/ *-commutative
Counts
4 → 453
Calls
4 calls:
643.0ms
(* (sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0)) w0)
337.0ms
(sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0))
13.0ms
(/ (* M D) (* 2.0 d))
52.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h)))

series2.6s

Counts
4 → 12
Calls
4 calls:
798.0ms
(* (sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0)) w0)
616.0ms
(sqrt (+ (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h))) 1.0))
53.0ms
(/ (* M D) (* 2.0 d))
1.1s
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l (- h)))

simplify978.0ms

Counts
465 → 465
Iterations
IterNodes
done5000
12244
0824

prune3.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize74.0ms

Local error

Found 4 expressions with local error:

3.8b
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (* (cbrt h) (cbrt h)))
4.0b
(sqrt (+ (* (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (* (cbrt h) (cbrt h))) (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt l) (- (cbrt h))))) 1.0))
7.0b
(/ (* M D) (* 2.0 d))
7.0b
(/ (* M D) (* 2.0 d))

rewrite650.0ms

Algorithm
rewrite-expression-head
Rules
173×add-exp-log
83×prod-exp
52×div-exp
39×add-cbrt-cube
20×pow-exp
19×cbrt-unprod
15×times-frac
13×associate-*l*
12×add-sqr-sqrt cbrt-undiv
10×pow1
8×*-un-lft-identity add-cube-cbrt
6×unpow-prod-down
4×expm1-log1p-u pow-to-exp log1p-expm1-u div-inv add-log-exp unswap-sqr
3×pow-prod-down sqrt-prod
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* sqr-pow
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* associate-*l/ *-commutative flip-+
Counts
4 → 130
Calls
4 calls:
59.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (* (cbrt h) (cbrt h)))
557.0ms
(sqrt (+ (* (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (* (cbrt h) (cbrt h))) (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt l) (- (cbrt h))))) 1.0))
18.0ms
(/ (* M D) (* 2.0 d))
11.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
816.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (* (cbrt h) (cbrt h)))
582.0ms
(sqrt (+ (* (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (* (cbrt h) (cbrt h))) (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt l) (- (cbrt h))))) 1.0))
54.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(/ (* M D) (* 2.0 d))

simplify1.8s

Counts
142 → 142
Iterations
IterNodes
done5000
24195
1869
0288

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

localize96.0ms

Local error

Found 4 expressions with local error:

7.0b
(/ (/ M (/ 2.0 D)) d)
14.4b
(cbrt (/ (/ M (/ 2.0 D)) d))
14.4b
(cbrt (/ (/ M (/ 2.0 D)) d))
14.4b
(cbrt (/ (/ M (/ 2.0 D)) d))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
1386×times-frac
639×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
408×cbrt-prod
56×div-inv
44×associate-/l*
13×add-cbrt-cube add-exp-log associate-/r/
6×cbrt-undiv div-exp
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×cbrt-div associate-/r* pow1/3
1×clear-num frac-2neg associate-/l/
Counts
4 → 639
Calls
4 calls:
20.0ms
(/ (/ M (/ 2.0 D)) d)
20.0ms
(cbrt (/ (/ M (/ 2.0 D)) d))
12.0ms
(cbrt (/ (/ M (/ 2.0 D)) d))
13.0ms
(cbrt (/ (/ M (/ 2.0 D)) d))

series949.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (/ M (/ 2.0 D)) d)
160.0ms
(cbrt (/ (/ M (/ 2.0 D)) d))
575.0ms
(cbrt (/ (/ M (/ 2.0 D)) d))
171.0ms
(cbrt (/ (/ M (/ 2.0 D)) d))

simplify876.0ms

Counts
651 → 651
Iterations
IterNodes
done5000
11534
0742

prune10.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.1b

regimes2.1s

Accuracy

15.6% (3.0b remaining)

Error of 7.7b against oracle of 4.7b and baseline of 8.3b

bsearch3.0ms

simplify22.0ms

Iterations
IterNodes
done52
352
250
144
032

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.6s9334×body80valid
387.0ms3069×body80nan