Details

sample49.0ms

Algorithm

intervals

Results

16.0ms	306×	body	80	valid
9.0ms	104×	body	80	nan

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	80	18
3	176	18
4	413	18
5	1262	18
6	4868	18
done	5000	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize14.0ms

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))

rewrite35.0ms

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))))
4.0ms	(/ (* M D) (* 2.0 d))
15.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

403.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
364.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms	(/ (* M D) (* 2.0 d))
679.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify826.0ms

Counts

133 → 133

Iterations

Useful iterations: 2 (262.0ms)

Iter	Nodes	Cost
0	244	2427
1	622	2198
2	2336	2040
done	5000	2040

prune453.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize17.0ms

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))

rewrite33.0ms

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))
5.0ms	(/ (* 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:

360.0ms	(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))
26.0ms	(/ (* M D) (* 2.0 d))
708.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify814.0ms

Counts

130 → 130

Iterations

Useful iterations: 2 (249.0ms)

Iter	Nodes	Cost
0	217	2546
1	589	2124
2	2322	1902
done	5000	1902

prune452.0ms

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))

series1.5s

Counts

4 → 12

Calls

4 calls:

718.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
693.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
27.0ms	(/ (* M D) (* 2.0 d))
32.0ms	(/ (* M D) (* 2.0 d))

simplify725.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	194	1838
1	509	1732
2	2166	1490
done	5000	1490

prune403.0ms

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 (/ (* (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))

rewrite16.0ms

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:

4.0ms	(/ (* 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))

series1.5s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
491.0ms	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
495.0ms	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
500.0ms	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))

simplify870.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (297.0ms)

Iter	Nodes	Cost
0	138	1761
1	316	1738
2	1316	1566
done	5000	1566

prune420.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.3b

regimes780.0ms

Accuracy

-28.8% (2.0b remaining)

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

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

sample1.2s

Algorithm

intervals

Results

505.0ms	9329×	body	80	valid
181.0ms	3112×	body	80	nan