Details

Time bar (total: 39.3s)

sample59.0ms

Algorithm
intervals
Results
20.0ms302×body80valid
5.0ms68×body80nan

simplify2.8s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize68.0ms

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))

rewrite100.0ms

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:
33.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
11.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.0ms
(/ (* M D) (* 2.0 d))
37.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
657.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
539.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
52.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify2.3s

Counts
133 → 133
Iterations
IterNodes
done5000
23154
1643
0244

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.2b

localize49.0ms

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))

rewrite82.0ms

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)))))
22.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
611.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
36.0ms
(/ (* M D) (* 2.0 d))
49.0ms
(/ (* M D) (* 2.0 d))
977.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify2.7s

Counts
130 → 130
Iterations
IterNodes
done5002
23030
1606
0217

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.9b

localize82.0ms

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))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
64×prod-exp
40×add-cbrt-cube
25×div-exp
22×associate-*r*
20×times-frac cbrt-unprod
19×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
11×cbrt-undiv
10×pow1 pow-exp
9×cbrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down sqrt-prod div-inv
2×pow-to-exp clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* associate-*r/ *-commutative flip--
Counts
4 → 123
Calls
4 calls:
9.0ms
(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)))))
20.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(/ (* M D) (* 2.0 d))
203.0ms
(* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt h)) (cbrt h)) (/ (cbrt h) l))

series2.1s

Counts
4 → 12
Calls
4 calls:
587.0ms
(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)))))
56.0ms
(/ (* M D) (* 2.0 d))
36.0ms
(/ (* M D) (* 2.0 d))
1.4s
(* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt h)) (cbrt h)) (/ (cbrt h) l))

simplify3.9s

Counts
135 → 135
Iterations
IterNodes
done5000
24632
1748
0252

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.6b

localize198.0ms

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))

rewrite485.0ms

Algorithm
rewrite-expression-head
Rules
283×add-exp-log
172×prod-exp
66×associate-*r*
55×times-frac div-exp
52×add-cbrt-cube
43×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
40×cbrt-unprod
30×pow-exp
27×cbrt-prod
19×pow1
13×cbrt-undiv
9×pow-prod-down
6×pow-to-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*l* associate-*r/ *-commutative
1×clear-num associate-/r* frac-2neg associate-/l*
Counts
4 → 203
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
163.0ms
(* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt h)) (cbrt h)) (/ (cbrt h) l))
134.0ms
(* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt h)) (cbrt h)) (/ (cbrt h) l))
163.0ms
(* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt h)) (cbrt h)) (/ (cbrt h) l))

series3.2s

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt h)) (cbrt h)) (/ (cbrt h) l))
1.0s
(* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt h)) (cbrt h)) (/ (cbrt h) l))
1.0s
(* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt h)) (cbrt h)) (/ (cbrt h) l))

simplify3.7s

Counts
215 → 215
Iterations
IterNodes
done5001
24368
1671
0218

prune3.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.6b

regimes3.0s

Accuracy

16.8% (1.7b remaining)

Error of 9.5b against oracle of 7.8b and baseline of 9.8b

bsearch134.0ms

Steps
ItersRangePoint
0
-3.2552887468857e-311
-8.1311866652206e-312
-2.0342037067041e-311
10
-inf.0
-5.499013127196744e+290
-1.772133656628061e+308

simplify28.0ms

Iterations
IterNodes
done37
137
028

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.4s9319×body80valid
342.0ms3144×body80nan