Details

sample59.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	295	48
3	1832	48
done	5000	48

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.7b

localize37.0ms

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))))
38.7b	(/ (/ (* (* 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))
45.4b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.2s

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:

263.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
160.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
491.0ms	(/ (/ (* (* 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))
227.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
146.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s	(/ (/ (* (* 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))
272.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify846.0ms

Counts

220 → 220

Iterations

Useful iterations: done (827.0ms)

Iter	Nodes	Cost
0	366	12421
1	1370	11478
done	5001	9638

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 36.7b

localize46.0ms

Local error

Found 4 expressions with local error:

37.6b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
37.6b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
38.1b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
38.1b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
8×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `associate-*r/` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
2×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 108

Calls

4 calls:

80.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
69.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
5.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
5.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series667.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
134.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
205.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
222.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify1.1s

Counts

120 → 120

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	109	2616
1	271	2574
2	1439	2282
done	5002	2270

prune939.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 36.7b

localize42.0ms

Local error

Found 4 expressions with local error:

37.6b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
37.7b	(/ (fma 2.0 i (+ alpha beta)) (* i (+ (+ alpha beta) i)))
38.1b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
38.1b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r` `associate-/l`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `associate-*r/` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `associate-/l/`

Counts

4 → 108

Calls

4 calls:

56.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
60.0ms	(/ (fma 2.0 i (+ alpha beta)) (* i (+ (+ alpha beta) i)))
10.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
6.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series632.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
128.0ms	(/ (fma 2.0 i (+ alpha beta)) (* i (+ (+ alpha beta) i)))
175.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
169.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify1.4s

Counts

120 → 120

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	140	2614
1	361	2575
2	1991	2285
done	5000	2275

prune930.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 36.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
37.6b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
38.1b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
38.7b	(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
32×	`add-sqr-sqrt`
29×	`times-frac`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-undiv` `div-exp`
17×	`prod-exp` `cbrt-unprod`
13×	`associate-r`
10×	`associate-/r*`
7×	`associate-l`
6×	`pow1`
5×	`div-inv` `associate-/l/` `associate-/l*`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `associate-*l/` `associate-/r/` `difference-of-squares` `unswap-sqr`
1×	`flip3--` `flip3-+` `pow-prod-down` `*-commutative` `flip--` `flip-+`

Counts

4 → 142

Calls

4 calls:

107.0ms	(* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
71.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
9.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
265.0ms	(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

231.0ms	(* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
119.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
169.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
1.2s	(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

simplify564.0ms

Counts

154 → 154

Iterations

Useful iterations: done (558.0ms)

Iter	Nodes	Cost
0	234	6323
1	735	6127
done	5000	4785

prune748.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 36.7b

regimes275.0ms

Accuracy

3.1% (3.7b remaining)

Error of 38.3b against oracle of 34.5b and baseline of 38.4b

bsearch210.0ms

Steps

Iters	Range		Point
2	2.9890207141089673e+150	3.2088919848491803e+150	3.1814080760066536e+150
8	5.522922348167397e+137	5.889816599354321e+140	2.677113738334714e+139
7	1.1669666060540711e+85	2.123166983468196e+86	1.980179602823052e+86

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	176
1	54	176
done	54	176

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
356.0ms	8000×	pre	80	true