Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

266×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	65	15
4	96	15
5	130	15
6	163	15
7	239	15
8	396	15
9	710	15
10	1479	15
11	4000	15
done	5001	15

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.0b	(* z (- t a))
1.4b	(+ (* x y) (* z (- t a)))
21.8b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
54×	`prod-diff`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
44×	`associate-+r+`
33×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `sub-neg`
5×	`associate-r`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`+-commutative` `associate-*r/` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 153

Calls

4 calls:

6.0ms	(+ y (* z (- b y)))
12.0ms	(* z (- t a))
6.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ y (* z (- b y)))
40.0ms	(* z (- t a))
51.0ms	(+ (* x y) (* z (- t a)))
366.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify829.0ms

Counts

165 → 165

Iterations

Useful iterations: done (824.0ms)

Iter	Nodes	Cost
0	279	2673
1	579	2249
2	1529	1865
done	5000	1847

prune550.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.9b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (fma (- b y) z y) (fma z (- t a) (* x y))))
0.8b	(fma z (- t a) (* x y))
21.8b	(/ (fma (- b y) z y) (fma z (- t a) (* x y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `associate-/r*`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `associate-/r/` `fma-udef` `inv-pow`

Counts

3 → 117

Calls

3 calls:

9.0ms	(/ 1 (/ (fma (- b y) z y) (fma z (- t a) (* x y))))
0.0ms	(fma z (- t a) (* x y))
2.0ms	(/ (fma (- b y) z y) (fma z (- t a) (* x y)))

series1.8s

Counts

3 → 9

Calls

3 calls:

1.6s	(/ 1 (/ (fma (- b y) z y) (fma z (- t a) (* x y))))
59.0ms	(fma z (- t a) (* x y))
186.0ms	(/ (fma (- b y) z y) (fma z (- t a) (* x y)))

simplify2.2s

Counts

126 → 126

Iterations

Useful iterations: 3 (823.0ms)

Iter	Nodes	Cost
0	170	3177
1	350	3005
2	842	2682
3	2383	2664
done	5001	2664

prune372.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.7b	(/ 1 (fma (- b y) z y))
0.8b	(fma z (- t a) (* x y))
21.5b	(* (/ 1 (fma (- b y) z y)) (fma z (- t a) (* x y)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-l`
10×	`add-cbrt-cube`
6×	`pow1`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `associate-r` `associate-/r` `fma-udef` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `pow-flip` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `inv-pow`

Counts

3 → 82

Calls

3 calls:

2.0ms	(/ 1 (fma (- b y) z y))
0.0ms	(fma z (- t a) (* x y))
10.0ms	(* (/ 1 (fma (- b y) z y)) (fma z (- t a) (* x y)))

series1.5s

Counts

3 → 9

Calls

3 calls:

108.0ms	(/ 1 (fma (- b y) z y))
53.0ms	(fma z (- t a) (* x y))
1.3s	(* (/ 1 (fma (- b y) z y)) (fma z (- t a) (* x y)))

simplify1.8s

Counts

91 → 91

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	113	1467
1	240	1358
2	637	1174
3	2099	1174
done	5000	1174

prune283.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (fma (- b y) z y))
0.8b	(fma z (- t a) (* x y))
1.0b	(/ 1 (fma z (- t a) (* x y)))
21.1b	(/ (/ 1 (fma (- b y) z y)) (/ 1 (fma z (- t a) (* x y))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

439×	`times-frac`
216×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`add-exp-log`
36×	`div-exp`
31×	`div-inv`
20×	`add-cbrt-cube`
19×	`associate-/r` `associate-/l`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`associate-/r/` `fma-udef` `associate-/l/`

Counts

4 → 305

Calls

4 calls:

2.0ms	(/ 1 (fma (- b y) z y))
0.0ms	(fma z (- t a) (* x y))
2.0ms	(/ 1 (fma z (- t a) (* x y)))
11.0ms	(/ (/ 1 (fma (- b y) z y)) (/ 1 (fma z (- t a) (* x y))))

series1.5s

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ 1 (fma (- b y) z y))
47.0ms	(fma z (- t a) (* x y))
67.0ms	(/ 1 (fma z (- t a) (* x y)))
1.2s	(/ (/ 1 (fma (- b y) z y)) (/ 1 (fma z (- t a) (* x y))))

simplify3.1s

Counts

317 → 317

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	414	10017
1	1186	9022
2	2781	7812
done	5000	7758

prune481.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 15.1b

regimes485.0ms

Accuracy

71.7% (2.4b remaining)

Error of 17.8b against oracle of 15.4b and baseline of 23.8b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	108
1	42	102
done	42	102

end0.0ms

sample657.0ms

Algorithm

intervals

Results

361.0ms

8403×

body

valid