Details

sample43.0ms

Algorithm

intervals

Results

16.0ms	306×	body	80	valid
6.0ms	104×	body	80	nan

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	80	18
3	172	18
4	405	18
5	1246	18
6	4859	18
done	5000	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize20.0ms

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))

rewrite34.0ms

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:

9.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms	(/ (* M D) (* 2.0 d))
14.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.7s

Counts

4 → 12

Calls

4 calls:

406.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
354.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
30.0ms	(/ (* M D) (* 2.0 d))
879.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify765.0ms

Counts

125 → 125

Iterations

Useful iterations: 2 (254.0ms)

Iter	Nodes	Cost
0	236	2311
1	610	2083
2	2308	1927
done	5000	1927

prune413.0ms

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))

rewrite31.0ms

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:

2.0ms	(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))

series1.1s

Counts

4 → 12

Calls

4 calls:

390.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
28.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
699.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify802.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (236.0ms)

Iter	Nodes	Cost
0	211	2420
1	579	2019
2	2296	1799
done	5001	1799

prune434.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

localize22.0ms

Local error

Found 4 expressions with local error:

5.2b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
6.4b	(/ (* M D) (* 2.0 d))
6.4b	(/ (* M D) (* 2.0 d))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

177×	`add-exp-log`
95×	`prod-exp`
44×	`div-exp`
42×	`add-cbrt-cube`
25×	`pow-exp`
19×	`add-sqr-sqrt`
16×	`associate-r`
15×	`cbrt-unprod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`cbrt-undiv` `associate-l`
8×	`rec-exp` `1-exp`
6×	`pow1` `unpow-prod-down`
5×	`pow-to-exp`
4×	`div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*` `sqr-pow`
1×	`associate-*r/` `pow-prod-down` `un-div-inv`

Counts

4 → 134

Calls

4 calls:

10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
17.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))

series1.5s

Counts

4 → 12

Calls

4 calls:

713.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
699.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
27.0ms	(/ (* M D) (* 2.0 d))
35.0ms	(/ (* M D) (* 2.0 d))

simplify796.0ms

Counts

146 → 146

Iterations

Useful iterations: 2 (266.0ms)

Iter	Nodes	Cost
0	238	2550
1	701	2214
2	2468	1920
done	5001	1920

prune425.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.3b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 69

Calls

4 calls:

4.0ms	(/ (* M D) (* 2.0 d))
3.0ms	(cbrt (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))
3.0ms	(cbrt (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))
7.0ms	(cbrt (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))

series1.6s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
537.0ms	(cbrt (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))
527.0ms	(cbrt (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))
519.0ms	(cbrt (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))

simplify677.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	134	1643
1	312	1620
2	1296	1448
done	5000	1448

prune409.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.3b

regimes822.0ms

Accuracy

-28% (2.0b remaining)

Error of 9.3b against oracle of 7.3b and baseline of 8.9b

bsearch47.0ms

Steps

Iters	Range		Point
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)

Iter	Nodes	Cost
0	28	52
1	37	49
done	37	49

end0.0ms

sample1.1s

Algorithm

intervals

Results

505.0ms	9329×	body	80	valid
177.0ms	3112×	body	80	nan