Details

Time bar (total: 1.1m)

sample107.0ms

Algorithm
intervals
Results
32.0ms289×body80valid
11.0ms96×body80nan

simplify9.8s

Counts
1 → 1
Iterations
IterNodes
done5000
64261
51442
4379
3165
279
136
017

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize59.0ms

Local error

Found 4 expressions with local error:

2.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.5b
(/ (* M D) (* 2.0 d))
6.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.4b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite137.0ms

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 insert-posit16 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 → 125
Calls
4 calls:
48.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
21.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
48.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series4.5s

Counts
4 → 12
Calls
4 calls:
1.5s
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
41.0ms
(/ (* M D) (* 2.0 d))
1.2s
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
1.8s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify4.2s

Counts
137 → 137
Iterations
IterNodes
done5462
22329
1630
0248

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.1b

localize87.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* M D) (* 2.0 d))
5.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.2b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
6.6b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

rewrite173.0ms

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×*-un-lft-identity add-cube-cbrt
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×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*r/ un-div-inv flip-- associate-/l*
Counts
4 → 140
Calls
4 calls:
30.0ms
(/ (* M D) (* 2.0 d))
35.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
77.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
16.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

series5.1s

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* M D) (* 2.0 d))
1.9s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
1.9s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
1.3s
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

simplify4.5s

Counts
152 → 152
Iterations
IterNodes
done5016
22650
1735
0281

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.0b

localize84.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))
6.2b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
6.6b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
1381×add-exp-log
896×prod-exp
362×div-exp
300×pow-exp
60×pow-to-exp
57×rec-exp 1-exp
49×add-cbrt-cube
20×cbrt-unprod
13×add-sqr-sqrt associate-*r*
12×*-un-lft-identity add-cube-cbrt
11×cbrt-undiv times-frac
7×pow1
4×expm1-log1p-u insert-posit16 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/ un-div-inv *-commutative flip--
Counts
4 → 328
Calls
4 calls:
24.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(/ (* M D) (* 2.0 d))
218.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
11.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))

series3.1s

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ (* M D) (* 2.0 d))
52.0ms
(/ (* M D) (* 2.0 d))
1.9s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
1.2s
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))

simplify5.2s

Counts
340 → 340
Iterations
IterNodes
done5048
22771
1937
0427

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.8b

localize88.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))
6.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
14×add-sqr-sqrt
12×div-exp
9×associate-*l* cbrt-unprod
8×cbrt-undiv *-un-lft-identity add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-*r* sqrt-prod div-inv unswap-sqr
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square sqrt-pow1 flip3-- pow1/2 *-commutative flip--
Counts
4 → 100
Calls
4 calls:
58.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
17.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
20.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))

series3.2s

Counts
4 → 12
Calls
4 calls:
1.9s
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
44.0ms
(/ (* M D) (* 2.0 d))
59.0ms
(/ (* M D) (* 2.0 d))
1.2s
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))

simplify3.2s

Counts
112 → 112
Iterations
IterNodes
done5000
21756
1456
0180

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.8b

regimes8.0s

Accuracy

-8.4% (1.5b remaining)

Error of 8.6b against oracle of 7.1b and baseline of 8.5b

bsearch6.0ms

simplify28.0ms

Iterations
IterNodes
done36
136
027

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s9320×body80valid
709.0ms3180×body80nan