Details

Time bar (total: 8.5s)

sample46.0ms

Algorithm
intervals
Results
15.0ms293×body80valid
6.0ms111×body80nan

simplify54.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019
done50019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.6b
(/ (* M D) (* 2.0 d))
5.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite71.0ms

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:
20.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
12.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
30.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
440.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
29.0ms
(/ (* M D) (* 2.0 d))
392.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
691.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06091075
12742997
25002994
done5002994

prune388.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.5b

localize18.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.1b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.6b
(/ (* M D) (* 2.0 d))
5.9b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 128
Calls
4 calls:
23.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
41.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
12.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

series1.8s

Counts
4 → 12
Calls
4 calls:
735.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
698.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
28.0ms
(/ (* M D) (* 2.0 d))
385.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

simplify86.0ms

Counts
140 → 140
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07521136
134671014
250011001
done50011001

prune383.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.2b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune23.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.2b

localize21.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (* M D) (* 2.0 d))
5.6b
(/ (* M D) (* 2.0 d))
5.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
9.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite66.0ms

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×add-cube-cbrt *-un-lft-identity
13×associate-*r*
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
7×unpow-prod-down
6×unswap-sqr
5×pow1
4×div-inv add-log-exp
3×sqrt-prod sqr-pow
2×pow-to-exp 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 → 110
Calls
4 calls:
14.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
30.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))
393.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
721.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify68.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
05761133
125821013
250011012
done50011012

prune387.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.0b

regimes808.0ms

Accuracy

-90.5% (2.3b remaining)

Error of 9.5b against oracle of 7.2b and baseline of 8.4b

bsearch39.0ms

Steps
ItersRangePoint
7
2.776751705813962e+270
4.624845619350977e+271
3.714656130753053e+271

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03216
13216
done3216

end0.0ms

sample1.2s

Algorithm
intervals
Results
484.0ms9258×body80valid
164.0ms3051×body80nan