Details

Time bar (total: 16.4s)

sample46.0ms

Algorithm
intervals
Results
19.0ms299×body80valid
6.0ms112×body80nan

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28018
317618
441318
5126218
6486818
done500018

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b
(/ (* M D) (* 2.0 d))
7.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite38.0ms

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:
9.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
402.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
360.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
674.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify862.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (275.0ms)

IterNodesCost
02442427
16222198
223362040
done50002040

prune436.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.2b

localize18.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.5b
(/ (* M D) (* 2.0 d))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 104
Calls
4 calls:
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
11.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.0ms
(/ (* M D) (* 2.0 d))

series1.8s

Counts
4 → 12
Calls
4 calls:
703.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
725.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
362.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
28.0ms
(/ (* M D) (* 2.0 d))

simplify1.0s

Counts
116 → 116
Iterations

Useful iterations: 2 (223.0ms)

IterNodesCost
02321901
15721737
223331581
done50001581

prune381.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

5.4b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.5b
(/ (* M D) (* 2.0 d))
5.5b
(/ (* M D) (* 2.0 d))
5.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
16×add-sqr-sqrt
12×div-exp
10×*-un-lft-identity
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-*r* div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 98
Calls
4 calls:
11.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(/ (* M D) (* 2.0 d))
11.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.1s

Counts
4 → 12
Calls
4 calls:
369.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
27.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))
713.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify792.0ms

Counts
110 → 110
Iterations

Useful iterations: 2 (167.0ms)

IterNodesCost
01812080
14561675
217751485
done50001485

prune408.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize25.0ms

Local error

Found 4 expressions with local error:

5.4b
(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.5b
(/ (* 2.0 d) (* M D))
5.5b
(/ (* M D) (* 2.0 d))
5.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
16×add-sqr-sqrt
12×div-exp
10×*-un-lft-identity
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-*r* div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 98
Calls
4 calls:
10.0ms
(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.0ms
(/ (* 2.0 d) (* M D))
4.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.1s

Counts
4 → 12
Calls
4 calls:
304.0ms
(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
32.0ms
(/ (* 2.0 d) (* M D))
27.0ms
(/ (* M D) (* 2.0 d))
715.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify960.0ms

Counts
110 → 110
Iterations

Useful iterations: 2 (221.0ms)

IterNodesCost
02062136
15381975
223991783
done50011783

prune409.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

regimes831.0ms

Accuracy

0% (1.8b remaining)

Error of 9.4b against oracle of 7.6b and baseline of 9.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02434
13134
done3134

end0.0ms

sample1.1s

Algorithm
intervals
Results
495.0ms9351×body80valid
174.0ms3125×body80nan