Details

sample79.0ms

Algorithm

intervals

Results

37.0ms	363×	body	80	valid
12.0ms	129×	body	80	nan

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	12	15
1	24	15
2	53	13
3	107	12
4	254	12
5	735	12
6	2729	12
done	5001	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
1.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
7×	`associate-r`
6×	`fma-def` `prod-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `div-exp` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `times-frac` `associate-l` `associate-/r*` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `sqr-pow`
1×	`associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 88

Calls

4 calls:

12.0ms	(+ 1.0 (* 10.0 k))
25.0ms	(* a (pow k m))
52.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
77.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ 1.0 (* 10.0 k))
104.0ms	(* a (pow k m))
33.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
183.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts

100 → 100

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	179	1340
1	471	1136
2	1627	982
done	5000	933

prune412.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(/ (/ (* a (pow k m)) (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
16.3b	(sqrt (fma k (+ 10.0 k) 1.0))
16.3b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite506.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
60×	`sqrt-prod`
53×	`add-sqr-sqrt`
50×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/l*`
9×	`div-exp` `add-log-exp`
8×	`div-inv`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `prod-exp` `sum-log` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `hypot-def` `associate-/l/`

Counts

4 → 150

Calls

4 calls:

394.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
44.0ms	(/ (/ (* a (pow k m)) (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
51.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
278.0ms	(/ (/ (* a (pow k m)) (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
69.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
85.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.4s

Counts

162 → 162

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	282	4930
1	710	4149
2	2205	3497
done	5000	3384

prune777.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

16.3b	(sqrt (* (* (cbrt (fma k (+ 10.0 k) 1.0)) (cbrt (fma k (+ 10.0 k) 1.0))) (cbrt (fma k (+ 10.0 k) 1.0))))
16.8b	(cbrt (fma k (+ 10.0 k) 1.0))
16.8b	(cbrt (fma k (+ 10.0 k) 1.0))
16.8b	(cbrt (fma k (+ 10.0 k) 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 65

Calls

4 calls:

37.0ms	(sqrt (* (* (cbrt (fma k (+ 10.0 k) 1.0)) (cbrt (fma k (+ 10.0 k) 1.0))) (cbrt (fma k (+ 10.0 k) 1.0))))
1.0ms	(cbrt (fma k (+ 10.0 k) 1.0))
1.0ms	(cbrt (fma k (+ 10.0 k) 1.0))
1.0ms	(cbrt (fma k (+ 10.0 k) 1.0))

series557.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (* (* (cbrt (fma k (+ 10.0 k) 1.0)) (cbrt (fma k (+ 10.0 k) 1.0))) (cbrt (fma k (+ 10.0 k) 1.0))))
161.0ms	(cbrt (fma k (+ 10.0 k) 1.0))
141.0ms	(cbrt (fma k (+ 10.0 k) 1.0))
155.0ms	(cbrt (fma k (+ 10.0 k) 1.0))

simplify3.2s

Counts

77 → 77

Iterations

Useful iterations: 4 (2.0s)

Iter	Nodes	Cost
0	106	1130
1	224	993
2	539	778
3	1408	727
4	4404	720
done	5000	720

prune436.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (* a (pow k m)) (cbrt (pow (sqrt (fma k (+ 10.0 k) 1.0)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
16.3b	(sqrt (fma k (+ 10.0 k) 1.0))
16.3b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
21.7b	(cbrt (pow (sqrt (fma k (+ 10.0 k) 1.0)) 3))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

297×	`times-frac`
144×	`cbrt-prod`
132×	`sqrt-prod`
115×	`add-sqr-sqrt`
112×	`add-cube-cbrt` `*-un-lft-identity`
48×	`unpow-prod-down` `cube-prod`
25×	`associate-/l*`
20×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`div-exp`
8×	`cube-mult` `unpow3` `div-inv` `sqr-pow`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip-+`
1×	`pow-to-exp` `frac-2neg` `pow1/3` `pow-exp` `clear-num` `rem-cbrt-cube` `cbrt-unprod` `hypot-def` `associate-/l/`

Counts

4 → 266

Calls

4 calls:

109.0ms	(/ (/ (* a (pow k m)) (cbrt (pow (sqrt (fma k (+ 10.0 k) 1.0)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
2.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
25.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(cbrt (pow (sqrt (fma k (+ 10.0 k) 1.0)) 3))

series471.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(/ (/ (* a (pow k m)) (cbrt (pow (sqrt (fma k (+ 10.0 k) 1.0)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
64.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
64.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
98.0ms	(cbrt (pow (sqrt (fma k (+ 10.0 k) 1.0)) 3))

simplify1.7s

Counts

278 → 278

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	389	10865
1	878	8640
2	2502	6287
done	5000	6107

prune781.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes126.0ms

Accuracy

98.6% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch73.0ms

Steps

Iters	Range		Point
9	5.026229641937241e+135	1.4970672528079013e+142	1.4423024704689428e+138

simplify13.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	60
1	44	60
2	48	60
3	55	60
4	57	60
done	57	60

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.7s	11970×	body	80	valid
340.0ms	4494×	body	80	nan