Details

Time bar (total: 25.0s)

sample104.0ms

Algorithm
intervals
Results
38.0ms304×body80valid
11.0ms91×body80nan

simplify6.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28118
318018
443218
5122118
6469218
done500018

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.1b

localize34.0ms

Local error

Found 4 expressions with local error:

2.1b
(* 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))))
5.5b
(/ (* M D) (* 2.0 d))
6.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite158.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u 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 → 121
Calls
4 calls:
37.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
15.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
26.0ms
(/ (* M D) (* 2.0 d))
72.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
645.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
556.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
47.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.5s

Counts
133 → 133
Iterations

Useful iterations: 2 (446.0ms)

IterNodesCost
02442427
15982198
222962040
done50022040

prune682.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.5b

localize66.0ms

Local error

Found 4 expressions with local error:

2.1b
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
3.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (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)))))
5.5b
(/ (* M D) (* 2.0 d))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
179×add-exp-log
88×prod-exp
52×div-exp
28×add-cbrt-cube
25×pow-exp
23×add-sqr-sqrt
14×cbrt-unprod
12×associate-*l*
11×add-cube-cbrt *-un-lft-identity associate-*r*
8×cbrt-undiv unswap-sqr
7×pow1 unpow-prod-down sqrt-prod
6×times-frac
5×pow-to-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r/ div-inv sqr-pow
2×flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 137
Calls
4 calls:
36.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
108.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (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)))))
16.0ms
(/ (* M D) (* 2.0 d))

series2.3s

Counts
4 → 12
Calls
4 calls:
729.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
892.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
609.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
37.0ms
(/ (* M D) (* 2.0 d))

simplify1.6s

Counts
149 → 149
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02834249
17223804
229642874
done50002618

prune774.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.0b

localize44.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
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)))))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))

rewrite127.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 134
Calls
4 calls:
81.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
7.0ms
(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)))))
13.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* M D) (* 2.0 d))

series1.4s

Counts
4 → 12
Calls
4 calls:
685.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
622.0ms
(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)))))
39.0ms
(/ (* M D) (* 2.0 d))
57.0ms
(/ (* M D) (* 2.0 d))

simplify1.5s

Counts
146 → 146
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02563956
16713336
228842664
done50012514

prune767.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.0b

localize49.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* M D) (* 2.0 d))
16.4b
(cbrt (/ (* M D) (* 2.0 d)))
16.4b
(cbrt (/ (* M D) (* 2.0 d)))
16.4b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log add-cbrt-cube
15×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-undiv expm1-log1p-u times-frac div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3
1×frac-2neg clear-num associate-/r* associate-/l*
Counts
4 → 71
Calls
4 calls:
17.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(cbrt (/ (* M D) (* 2.0 d)))
6.0ms
(cbrt (/ (* M D) (* 2.0 d)))
6.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* M D) (* 2.0 d))
113.0ms
(cbrt (/ (* M D) (* 2.0 d)))
151.0ms
(cbrt (/ (* M D) (* 2.0 d)))
158.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify672.0ms

Counts
83 → 83
Iterations

Useful iterations: done (668.0ms)

IterNodesCost
01061014
1242991
21044867
done5000849

prune775.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.0b

regimes803.0ms

Accuracy

0% (2.0b remaining)

Error of 9.9b against oracle of 7.9b and baseline of 9.9b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02646
13246
done3246

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s9379×body80valid
413.0ms3226×body80nan