Details

sample61.0ms

Algorithm

intervals

Results

35.0ms

268×

body

valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
11	4203
10	1582
9	731
8	425
7	258
6	185
5	149
4	115
3	75
2	43
1	24
0	14

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(+ y (* z (- b y)))
0.5b	(+ (* x y) (* z (- t a)))
25.6b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite86.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `sub-neg`
5×	`associate-r`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-l` `associate-/l`
2×	`+-commutative` `sum-log` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 157

Calls

4 calls:

20.0ms	(* z (- t a))
13.0ms	(+ y (* z (- b y)))
9.0ms	(+ (* x y) (* z (- t a)))
41.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series673.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* z (- t a))
61.0ms	(+ y (* z (- b y)))
60.0ms	(+ (* x y) (* z (- t a)))
498.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify1.8s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	1683
1	655
0	283

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 25.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (/ (fma (- b y) z y) (fma y x (* z (- t a)))))
0.3b	(fma y x (* z (- t a)))
25.5b	(/ (fma (- b y) z y) (fma y x (* z (- t a))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
72×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
68×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`div-exp`
7×	`pow1`
6×	`div-inv` `associate-/l*`
5×	`associate-r`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`rec-exp` `clear-num` `sub-neg` `frac-2neg` `1-exp` `associate-*r/`
1×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 167

Calls

4 calls:

32.0ms	(* z (- t a))
10.0ms	(/ 1 (/ (fma (- b y) z y) (fma y x (* z (- t a)))))
0.0ms	(fma y x (* z (- t a)))
4.0ms	(/ (fma (- b y) z y) (fma y x (* z (- t a))))

series2.4s

Counts

4 → 12

Calls

4 calls:

67.0ms	(* z (- t a))
1.9s	(/ 1 (/ (fma (- b y) z y) (fma y x (* z (- t a)))))
87.0ms	(fma y x (* z (- t a)))
304.0ms	(/ (fma (- b y) z y) (fma y x (* z (- t a))))

simplify2.3s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
3	3205
2	1211
1	576
0	269

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.5b

localize44.0ms

Local error

Found 3 expressions with local error:

0.3b	(fma z (- t a) (* x y))
0.3b	(/ 1 (fma z (- b y) y))
25.4b	(* (/ 1 (fma z (- b y) y)) (fma z (- t a) (* x y)))

rewrite17.0ms

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` `insert-posit16` `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` `clear-num` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 85

Calls

3 calls:

0.0ms	(fma z (- t a) (* x y))
4.0ms	(/ 1 (fma z (- b y) y))
11.0ms	(* (/ 1 (fma z (- b y) y)) (fma z (- t a) (* x y)))

series825.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(fma z (- t a) (* x y))
81.0ms	(/ 1 (fma z (- b y) y))
689.0ms	(* (/ 1 (fma z (- b y) y)) (fma z (- t a) (* x y)))

simplify2.3s

Counts

94 → 94

Iterations

Iter	Nodes
done	5004
3	2325
2	659
1	253
0	116

prune557.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.5b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
25.6b	(/ (+ (* x y) (* z (- t a))) (fma (* (cbrt y) (cbrt y)) (cbrt y) (* z (- b y))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `pow1/3` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 74

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
2.0ms	(cbrt y)
39.0ms	(/ (+ (* x y) (* z (- t a))) (fma (* (cbrt y) (cbrt y)) (cbrt y) (* z (- b y))))

series1.4s

Counts

4 → 12

Calls

4 calls:

283.0ms	(cbrt y)
257.0ms	(cbrt y)
261.0ms	(cbrt y)
606.0ms	(/ (+ (* x y) (* z (- t a))) (fma (* (cbrt y) (cbrt y)) (cbrt y) (* z (- b y))))

simplify1.9s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	2815
2	645
1	210
0	97

prune602.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 12.5b

regimes879.0ms

Accuracy

17.1% (9.8b remaining)

Error of 20.5b against oracle of 10.7b and baseline of 22.5b

bsearch181.0ms

Steps

Iters	Range		Point
4	8.803690821578165e+192	1.3341101639438144e+193	8.879606465820762e+192
10	3.056103735942779e-289	4.513537496159142e-272	5.972417992529298e-285
7	-2.2877610580956455e-238	-1.4732887646823425e-240	-1.5073212909314457e-240
6	-5.964080283091801e+212	-4.451961833520596e+211	-5.062409672741701e+211

simplify8.0ms

Iterations

Iter	Nodes
done	39
1	39
0	34

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8411×

body

valid