Details

sample28.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify5.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (61.0ms)

Iter	Nodes	Cost
0	16	21
1	33	20
2	78	20
3	152	20
4	367	19
5	682	19
6	1142	19
7	2125	19
8	4012	19
done	5000	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.3b	(+ (* (+ x y) z) (* (+ t y) a))
2.8b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.8b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

10.0ms	(* (+ x y) z)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
39.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
82.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series823.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ x y) z)
56.0ms	(+ (* (+ x y) z) (* (+ t y) a))
108.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
637.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify815.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (249.0ms)

Iter	Nodes	Cost
0	194	2540
1	569	2317
2	2165	2102
done	5001	2102

prune509.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b))))))
0.5b	(fma a t (* y (- a b)))
1.3b	(fma z (+ x y) (fma a t (* y (- a b))))
24.9b	(/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b)))))

rewrite66.0ms

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×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef` `associate-/l/`
1×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 161

Calls

4 calls:

21.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b))))))
0.0ms	(fma a t (* y (- a b)))
0.0ms	(fma z (+ x y) (fma a t (* y (- a b))))
37.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

862.0ms	(/ 1 (/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b))))))
43.0ms	(fma a t (* y (- a b)))
112.0ms	(fma z (+ x y) (fma a t (* y (- a b))))
117.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma a t (* y (- a b)))))

simplify2.0s

Counts

173 → 173

Iterations

Useful iterations: 3 (925.0ms)

Iter	Nodes	Cost
0	190	5188
1	423	4825
2	1018	4452
3	4219	4420
done	5000	4420

prune455.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1) (/ (+ (+ x t) y) (fma z (+ x y) (fma y (- a b) (* t a)))))
1.3b	(fma z (+ x y) (fma y (- a b) (* t a)))
1.8b	(fma y (- a b) (* t a))
24.9b	(/ (+ (+ x t) y) (fma z (+ x y) (fma y (- a b) (* t a))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

242×	`*-un-lft-identity`
234×	`times-frac`
117×	`add-sqr-sqrt` `add-cube-cbrt`
75×	`distribute-lft-out`
60×	`sqrt-prod`
22×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef` `associate-/l/`
1×	`flip3-+` `associate-/r/` `flip-+`

Counts

4 → 215

Calls

4 calls:

23.0ms	(/ (sqrt 1) (/ (+ (+ x t) y) (fma z (+ x y) (fma y (- a b) (* t a)))))
0.0ms	(fma z (+ x y) (fma y (- a b) (* t a)))
0.0ms	(fma y (- a b) (* t a))
36.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma y (- a b) (* t a))))

series892.0ms

Counts

4 → 12

Calls

4 calls:

635.0ms	(/ (sqrt 1) (/ (+ (+ x t) y) (fma z (+ x y) (fma y (- a b) (* t a)))))
106.0ms	(fma z (+ x y) (fma y (- a b) (* t a)))
37.0ms	(fma y (- a b) (* t a))
114.0ms	(/ (+ (+ x t) y) (fma z (+ x y) (fma y (- a b) (* t a))))

simplify1.8s

Counts

227 → 227

Iterations

Useful iterations: 3 (775.0ms)

Iter	Nodes	Cost
0	230	8031
1	507	7148
2	1046	6660
3	3948	6598
done	5000	6598

prune482.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.3b	(+ (* (+ x y) z) (* (+ t y) a))
2.8b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.9b	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
10×	`associate-*l/`
7×	`pow1` `flip3-+` `flip-+`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `frac-add` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `associate-l` `prod-diff` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `diff-log` `1-exp` `sum-log` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `fma-def` `frac-2neg` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 133

Calls

4 calls:

18.0ms	(/ 1 (+ (+ x t) y))
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
38.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
133.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

series872.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1 (+ (+ x t) y))
56.0ms	(+ (* (+ x y) z) (* (+ t y) a))
107.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
646.0ms	(* (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (/ 1 (+ (+ x t) y)))

simplify880.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (231.0ms)

Iter	Nodes	Cost
0	207	2953
1	607	2553
2	2290	2268
done	5000	2268

prune434.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.1b

regimes648.0ms

Accuracy

46.5% (11.8b remaining)

Error of 16.3b against oracle of 4.4b and baseline of 26.5b

bsearch87.0ms

Steps

Iters	Range		Point
8	2.4068838490227673e+40	1.0542243044934032e+43	1.2918166468940466e+42
5	-6.289516594595149e+115	-1.85370030410588e+115	-1.880087478392796e+115

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	26	41
1	41	37
done	41	37

end0.0ms

sample674.0ms

Algorithm

intervals

Results

400.0ms

8000×

body

valid