Details

Time bar (total: 36.8s)

sample96.0ms

Algorithm
intervals
Results
43.0ms302×body80valid
8.0ms68×body80nan

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
017538
136538
281538
3181538
4460538
52702538
done5001538

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize63.0ms

Local error

Found 4 expressions with local error:

2.6b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.7b
(/ (* M D) (* 2.0 d))
11.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite89.0ms

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×*-un-lft-identity add-cube-cbrt
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 clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-/l*
Counts
4 → 121
Calls
4 calls:
22.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.0ms
(/ (* M D) (* 2.0 d))
45.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
608.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
590.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
51.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify2.4s

Counts
133 → 133
Iterations

Useful iterations: 2 (918.0ms)

IterNodesCost
024465872
164361356
2315460294
done500060334

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.3b

localize58.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (* M D) (* 2.0 d))
10.1b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
33×add-cbrt-cube
30×prod-exp
28×add-sqr-sqrt
23×div-exp
15×times-frac
14×*-un-lft-identity add-cube-cbrt
13×associate-*r*
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
7×unpow-prod-down
6×unswap-sqr
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×sqrt-prod sqr-pow
2×pow-to-exp clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 118
Calls
4 calls:
6.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
10.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
55.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
543.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
45.0ms
(/ (* M D) (* 2.0 d))
48.0ms
(/ (* M D) (* 2.0 d))
971.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify2.5s

Counts
130 → 130
Iterations

Useful iterations: 2 (905.0ms)

IterNodesCost
021758501
160654100
2303052398
done500252398

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.9b

localize63.0ms

Local error

Found 4 expressions with local error:

4.5b
(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 h) l)))))
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (* M D) (* 2.0 d))
7.1b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
173×add-exp-log
96×prod-exp
42×add-cbrt-cube
39×div-exp
22×associate-*r*
20×times-frac pow-exp cbrt-unprod
19×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
11×cbrt-undiv
9×cbrt-prod
7×pow1
4×expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp
3×sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 134
Calls
4 calls:
8.0ms
(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 h) l)))))
10.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(/ (* M D) (* 2.0 d))
100.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

series1.8s

Counts
4 → 12
Calls
4 calls:
604.0ms
(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 h) l)))))
37.0ms
(/ (* M D) (* 2.0 d))
46.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

simplify3.5s

Counts
146 → 146
Iterations

Useful iterations: done (3.5s)

IterNodesCost
026180694
182174130
2473870771
done500069996

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.8b

localize231.0ms

Local error

Found 4 expressions with local error:

5.7b
(/ (* M D) (* 2.0 d))
7.1b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
7.1b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
7.1b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

rewrite361.0ms

Algorithm
rewrite-expression-head
Rules
451×add-exp-log
268×prod-exp
97×div-exp
66×associate-*r*
60×pow-exp
58×add-cbrt-cube
55×times-frac
43×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
40×cbrt-unprod
27×cbrt-prod
13×cbrt-undiv
12×pow-to-exp
10×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*l* pow-prod-down associate-*r/ *-commutative
1×clear-num associate-/r* frac-2neg associate-/l*
Counts
4 → 236
Calls
4 calls:
10.0ms
(/ (* M D) (* 2.0 d))
96.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
110.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
121.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

series3.6s

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
1.4s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))
1.1s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (/ (cbrt h) l))

simplify3.9s

Counts
248 → 248
Iterations

Useful iterations: done (3.8s)

IterNodesCost
0227169004
1744153573
24424147011
done5001143966

prune2.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.8b

regimes2.4s

Accuracy

-25% (2.0b remaining)

Error of 10.2b against oracle of 8.2b and baseline of 9.8b

bsearch208.0ms

Steps
ItersRangePoint
8
-2.2551848476590714e-248
-2.311589734371419e-251
-4.723316040141831e-251
10
-inf.0
-5.499013127196744e+290
-1.772133656628061e+308

simplify13.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0311251
1401251
done401251

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.4s9319×body80valid
406.0ms3144×body80nan