Details

sample47.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	295	48
3	1651	48
done	5002	48

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.6b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
43.7b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 208

Calls

4 calls:

279.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
168.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
363.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
259.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.7s

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
156.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.2s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
307.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify823.0ms

Counts

220 → 220

Iterations

Useful iterations: done (813.0ms)

Iter	Nodes	Cost
0	366	12421
1	1232	11265
done	5000	9611

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 34.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
3.1b	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
34.6b	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
38.5b	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
61×	`add-exp-log` `add-cbrt-cube`
57×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
29×	`cbrt-undiv` `div-exp`
15×	`div-inv`
14×	`associate-/r` `associate-/l`
13×	`difference-of-squares`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `associate-/l/`
2×	`associate-*r/` `fma-udef`
1×	`pow2` `distribute-rgt-in` `flip3--` `distribute-lft-in` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 187

Calls

4 calls:

14.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
83.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
196.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
22.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.9s

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
257.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.3s	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
211.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify2.3s

Counts

199 → 199

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	330	10445
1	909	9614
2	3975	8391
done	5001	7837

prune995.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 32.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
5.1b	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
32.1b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
32.1b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
18×	`sqrt-prod`
15×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/r*`
6×	`pow1` `associate-/l*`
5×	`cbrt-undiv` `div-exp` `associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv`
1×	`associate-*r/`

Counts

4 → 101

Calls

4 calls:

14.0ms	(/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
49.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
2.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
2.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.3s

Counts

4 → 12

Calls

4 calls:

279.0ms	(/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
802.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
107.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
68.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify892.0ms

Counts

113 → 113

Iterations

Useful iterations: done (886.0ms)

Iter	Nodes	Cost
0	187	3044
1	426	2830
2	1434	2542
done	5001	2519

prune656.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 32.4b

localize65.0ms

Local error

Found 4 expressions with local error:

5.1b	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
32.1b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
32.1b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
32.1b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
7×	`pow1`
5×	`associate-/r/`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `associate-/l*`
2×	`frac-times` `flip3-+` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+`
1×	`frac-2neg` `associate-r/` `clear-num` `associate-/r` `div-inv`

Counts

4 → 75

Calls

4 calls:

40.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
3.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
3.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
17.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.0s

Counts

4 → 12

Calls

4 calls:

791.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
72.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
77.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
82.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify999.0ms

Counts

87 → 87

Iterations

Useful iterations: done (994.0ms)

Iter	Nodes	Cost
0	136	2025
1	349	1872
2	1260	1617
done	5000	1590

prune682.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 32.4b

regimes184.0ms

Accuracy

27.5% (2.8b remaining)

Error of 36.7b against oracle of 33.9b and baseline of 37.7b

bsearch88.0ms

Steps

Iters	Range		Point
7	2.685545803537547e+153	5.024291111426141e+154	1.3329238333719119e+154

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	137
1	40	137
done	40	137

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
275.0ms	8000×	pre	80	true