Details

sample27.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify920.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	265	48
3	1349	48
done	5002	48

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
0.1b	(* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i)))
0.1b	(* (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
55.9b	(/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
25×	`prod-exp` `cbrt-unprod`
21×	`pow1`
13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-undiv` `div-exp`
8×	`associate-*r/`
7×	`associate-r` `associate-l` `pow-prod-down`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `*-commutative`
2×	`flip3-+` `flip-+` `associate-/l/` `unswap-sqr`
1×	`pow2` `frac-2neg` `times-frac` `pow-plus` `clear-num` `associate-/r` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l`

Counts

4 → 113

Calls

4 calls:

3.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
34.0ms	(* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i)))
8.0ms	(* (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
47.0ms	(/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))))

series991.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
146.0ms	(* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i)))
431.0ms	(* (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
349.0ms	(/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))))

simplify1.2s

Counts

125 → 125

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	208	4905
1	643	4728
2	3420	3214
done	5001	3166

prune332.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 35.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
0.1b	(* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (/ (* i (+ (+ alpha beta) i)) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))))
41.1b	(/ (* i (+ (+ alpha beta) i)) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
41.1b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
22×	`add-sqr-sqrt`
18×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
13×	`pow1` `times-frac`
10×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
3×	`associate-*r/` `swap-sqr` `unswap-sqr`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `fma-udef` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `pow-plus` `associate-*l/` `pow-sqr` `pow-prod-up` `flip-+`

Counts

4 → 125

Calls

4 calls:

7.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
43.0ms	(* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (/ (* i (+ (+ alpha beta) i)) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))))
18.0ms	(/ (* i (+ (+ alpha beta) i)) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
3.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

series727.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
361.0ms	(* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (/ (* i (+ (+ alpha beta) i)) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))))
144.0ms	(/ (* i (+ (+ alpha beta) i)) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
157.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

simplify934.0ms

Counts

137 → 137

Iterations

Useful iterations: done (929.0ms)

Iter	Nodes	Cost
0	204	5500
1	600	5331
2	2642	3898
done	5000	3886

prune381.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
36.0b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
36.0b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
41.1b	(/ (* i (+ (+ alpha beta) i)) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
99×	`times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
28×	`swap-sqr`
22×	`associate-r` `associate-l`
21×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
9×	`unswap-sqr`
6×	`cbrt-undiv` `div-exp`
5×	`prod-exp` `cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-/r`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `flip3-+` `pow-plus` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `-commutative` `pow-prod-up` `flip-+` `associate-/l*`

Counts

4 → 162

Calls

4 calls:

23.0ms	(* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
19.0ms	(/ (* i (+ (+ alpha beta) i)) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
63.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
56.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
144.0ms	(/ (* i (+ (+ alpha beta) i)) (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))

simplify812.0ms

Counts

174 → 174

Iterations

Useful iterations: done (799.0ms)

Iter	Nodes	Cost
0	233	7278
1	696	6353
2	2456	5315
done	5001	5311

prune522.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
36.0b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
36.0b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
40.9b	(/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
99×	`times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
28×	`swap-sqr`
22×	`associate-r` `associate-l`
21×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
9×	`unswap-sqr`
6×	`cbrt-undiv` `div-exp`
5×	`prod-exp` `cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`pow2` `frac-times` `frac-2neg` `flip3-+` `pow-plus` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+`

Counts

4 → 162

Calls

4 calls:

27.0ms	(* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
11.0ms	(/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))
56.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
62.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
174.0ms	(/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i)))

simplify801.0ms

Counts

174 → 174

Iterations

Useful iterations: done (794.0ms)

Iter	Nodes	Cost
0	238	7276
1	693	6357
2	2415	5325
done	5000	5321

prune512.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.2b

regimes129.0ms

Accuracy

23.7% (4.4b remaining)

Error of 38.5b against oracle of 34.0b and baseline of 39.9b

bsearch66.0ms

Steps

Iters	Range		Point
9	1.5047751988170833e+141	2.1668113938075237e+147	2.134998786884618e+147

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	31	61
done	31	61

end0.0ms

sample688.0ms

Algorithm

intervals

Results

358.0ms	8000×	body	80	valid
140.0ms	8000×	pre	80	true