Details

sample41.0ms

Algorithm

intervals

Results

18.0ms	255×	body	80	valid
0.0ms	1×	body	160	valid

simplify5.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4082
7	1989
6	1145
5	750
4	496
3	200
2	79
1	33
0	16

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (+ z a) b) y)
0.5b	(fma a t (* (- (+ z a) b) y))
1.0b	(fma z x (fma a t (* (- (+ z a) b) y)))
25.9b	(/ (fma z x (fma a t (* (- (+ z a) b) y))) (+ x (+ y t)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-l`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/l*`
2×	`associate-*l/` `associate-/r/` `fma-udef` `distribute-lft-out--`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

112.0ms	(* (- (+ z a) b) y)
0.0ms	(fma a t (* (- (+ z a) b) y))
0.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
43.0ms	(/ (fma z x (fma a t (* (- (+ z a) b) y))) (+ x (+ y t)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (- (+ z a) b) y)
71.0ms	(fma a t (* (- (+ z a) b) y))
124.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
255.0ms	(/ (fma z x (fma a t (* (- (+ z a) b) y))) (+ x (+ y t)))

simplify1.0s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1026
1	286
0	133

prune651.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize11.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune73.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y)))))
0.5b	(fma a t (* (- (+ z a) b) y))
1.0b	(fma z x (fma a t (* (- (+ z a) b) y)))
26.0b	(/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
132×	`times-frac`
70×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef` `associate-/l/`
1×	`flip3-+` `associate-/r/` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 161

Calls

4 calls:

33.0ms	(/ 1 (/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y)))))
0.0ms	(fma a t (* (- (+ z a) b) y))
0.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
48.0ms	(/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y))))

series1.1s

Counts

4 → 12

Calls

4 calls:

742.0ms	(/ 1 (/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y)))))
88.0ms	(fma a t (* (- (+ z a) b) y))
141.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
145.0ms	(/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y))))

simplify2.2s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
3	4735
2	1346
1	458
0	188

prune1.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (- (+ z a) b))
0.5b	(fma a t (* y (- (+ z a) b)))
1.0b	(fma x z (fma a t (* y (- (+ z a) b))))
26.0b	(* (/ 1 (+ x (+ y t))) (fma x z (fma a t (* y (- (+ z a) b)))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
24×	`associate-l` `prod-diff`
17×	`times-frac`
16×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft-out`
15×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`associate-r`
8×	`pow1`
5×	`prod-exp`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-unprod`
2×	`sub-neg` `div-exp` `pow-prod-down` `associate--l+` `associate-r/` `associate-/r/` `-commutative` `distribute-lft-out--`
1×	`cbrt-undiv` `rec-exp` `flip3-+` `flip3--` `1-exp` `associate-*l/` `flip-+` `div-inv` `flip--` `difference-of-squares`

Counts

4 → 122

Calls

4 calls:

66.0ms	(* y (- (+ z a) b))
0.0ms	(fma a t (* y (- (+ z a) b)))
0.0ms	(fma x z (fma a t (* y (- (+ z a) b))))
59.0ms	(* (/ 1 (+ x (+ y t))) (fma x z (fma a t (* y (- (+ z a) b)))))

series930.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* y (- (+ z a) b))
67.0ms	(fma a t (* y (- (+ z a) b)))
120.0ms	(fma x z (fma a t (* y (- (+ z a) b))))
702.0ms	(* (/ 1 (+ x (+ y t))) (fma x z (fma a t (* y (- (+ z a) b)))))

simplify1.0s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	1432
1	499
0	211

prune559.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.1b

regimes807.0ms

Accuracy

46.3% (13.1b remaining)

Error of 17.4b against oracle of 4.3b and baseline of 28.7b

bsearch116.0ms

Steps

Iters	Range		Point
9	190.48575438544674	121699369396.6964	4617794.30963613
10	-1.3160740612192672e-52	-2.161818917794778e-63	-1.2430782448094334e-52

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

887.0ms	7998×	body	80	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid