Details

Time bar (total: 15.4s)

sample49.0ms

Algorithm
intervals
Results
18.0ms306×body80valid
6.0ms104×body80nan

simplify803.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28018
317718
443518
5135318
done500118

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize17.0ms

Local error

Found 4 expressions with local error:

2.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.4b
(/ (* M D) (* 2.0 d))
11.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite45.0ms

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:
11.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
19.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
514.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
441.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
38.0ms
(/ (* M D) (* 2.0 d))
817.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.1s

Counts
133 → 133
Iterations

Useful iterations: 2 (297.0ms)

IterNodesCost
02442427
16292200
226352040
done50002040

prune502.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize16.0ms

Local error

Found 4 expressions with local error:

3.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.4b
(/ (* M D) (* 2.0 d))
6.4b
(/ (* M D) (* 2.0 d))
8.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite32.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 118
Calls
4 calls:
3.0ms
(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))
4.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
439.0ms
(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
(/ (* M D) (* 2.0 d))
32.0ms
(/ (* M D) (* 2.0 d))
728.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify940.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (198.0ms)

IterNodesCost
02172546
15942124
224581902
done50001902

prune496.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

localize16.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.4b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.4b
(/ (* M D) (* 2.0 d))
6.4b
(/ (* M D) (* 2.0 d))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
35×add-cbrt-cube
30×prod-exp
24×div-exp
14×add-sqr-sqrt
10×cbrt-undiv pow-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×pow-to-exp sqr-pow
1×*-commutative
Counts
4 → 108
Calls
4 calls:
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.8s

Counts
4 → 12
Calls
4 calls:
884.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
806.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
28.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))

simplify753.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (205.0ms)

IterNodesCost
01941838
15181732
222601490
done50001490

prune517.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.3b

localize27.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ (* M D) (* 2.0 d))
23.5b
(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
23.5b
(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
23.5b
(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
16×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
4×pow1 cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3
1×frac-2neg clear-num associate-/r* associate-/l*
Counts
4 → 77
Calls
4 calls:
8.0ms
(/ (* M D) (* 2.0 d))
3.0ms
(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
3.0ms
(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
3.0ms
(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))

series1.9s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* M D) (* 2.0 d))
623.0ms
(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
598.0ms
(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
626.0ms
(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))

simplify450.0ms

Counts
89 → 89
Iterations

Useful iterations: 2 (125.0ms)

IterNodesCost
01381761
13161738
213311566
done50011566

prune508.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.3b

regimes866.0ms

Accuracy

-28.8% (2.0b remaining)

Error of 9.3b against oracle of 7.3b and baseline of 8.8b

bsearch49.0ms

Steps
ItersRangePoint
0
-6.0706316482279e-314
-1.976262583365e-323
-3.0353158251021e-314
6
-4.4879316068299356e+294
-6.981255098223496e+293
-4.434769257142831e+294

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02852
13749
done3749

end0.0ms

sample1.5s

Algorithm
intervals
Results
816.0ms9329×body80valid
195.0ms3112×body80nan