Details

Time bar (total: 26.7s)

sample68.0ms

Algorithm
intervals
Results
25.0ms288×body80valid
8.0ms95×body80nan

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01718
13618
28118
318118
445718
5267818
done500118

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize44.0ms

Local error

Found 4 expressions with local error:

3.6b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.3b
(/ (* M D) (* 2.0 d))
10.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite134.0ms

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:
43.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
16.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms
(/ (* M D) (* 2.0 d))
41.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
624.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
545.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
61.0ms
(/ (* M D) (* 2.0 d))
931.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.8s

Counts
133 → 133
Iterations

Useful iterations: 2 (473.0ms)

IterNodesCost
02442427
16442218
231322042
done50002042

prune675.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.7b

localize23.0ms

Local error

Found 4 expressions with local error:

3.6b
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
4.2b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.0b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.3b
(/ (* M D) (* 2.0 d))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
146×add-exp-log
81×prod-exp
36×div-exp
30×add-cbrt-cube
20×add-sqr-sqrt pow-exp
19×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×cbrt-unprod
10×times-frac
9×pow1
8×rec-exp 1-exp
7×sqrt-prod
6×cbrt-undiv
4×expm1-log1p-u pow-to-exp sqrt-div associate-*l* log1p-expm1-u add-log-exp
3×associate-*r/
2×flip3-- pow-prod-down *-commutative flip-- div-inv unswap-sqr
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r* un-div-inv associate-/l*
Counts
4 → 129
Calls
4 calls:
26.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
8.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
59.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
24.0ms
(/ (* M D) (* 2.0 d))

series2.3s

Counts
4 → 12
Calls
4 calls:
606.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
571.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
1.1s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
43.0ms
(/ (* M D) (* 2.0 d))

simplify3.1s

Counts
141 → 141
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02582785
17422425
238772030
done50012028

prune627.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.2b

localize21.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
3.6b
(* w0 (sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l)))))
4.2b
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))))
5.0b
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
130×add-exp-log
64×prod-exp
44×add-sqr-sqrt
40×times-frac
39×div-exp
34×associate-*l*
31×add-cube-cbrt *-un-lft-identity
28×unpow-prod-down
22×associate-*r*
20×pow-exp add-cbrt-cube
9×pow1
8×cbrt-unprod
7×rec-exp 1-exp sqrt-prod
6×unswap-sqr
5×pow-to-exp div-inv
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r/ *-commutative
2×cbrt-undiv flip3-- pow-prod-down flip-- sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ un-div-inv
Counts
4 → 156
Calls
4 calls:
51.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
35.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l)))))
16.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))))
99.0ms
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))

series3.0s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
579.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l)))))
510.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))))
898.0ms
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))

simplify3.5s

Counts
168 → 168
Iterations

Useful iterations: done (3.5s)

IterNodesCost
03373222
18612884
238322505
done50012503

prune702.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.9b

localize41.0ms

Local error

Found 4 expressions with local error:

5.3b
(/ (* M D) (* 2.0 d))
5.3b
(/ (* M D) (* 2.0 d))
7.2b
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
7.2b
(cbrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log add-cbrt-cube
8×cbrt-undiv cbrt-prod add-sqr-sqrt *-un-lft-identity div-exp prod-exp cbrt-unprod
6×add-cube-cbrt
4×pow1 expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
2×flip3-- frac-2neg times-frac pow1/3 clear-num associate-/r* flip-- div-inv associate-/l*
1×distribute-lft-out-- difference-of-squares
Counts
4 → 78
Calls
4 calls:
19.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.0ms
(cbrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

series726.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (* M D) (* 2.0 d))
40.0ms
(/ (* M D) (* 2.0 d))
327.0ms
(cbrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
322.0ms
(cbrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

simplify1.1s

Counts
90 → 90
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01301538
13291481
215401229
done50001217

prune465.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.9b

regimes655.0ms

Accuracy

38.7% (2.1b remaining)

Error of 9.2b against oracle of 7.1b and baseline of 10.5b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03684
14965
done4965

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s9242×body80valid
322.0ms3158×body80nan