Details

sample70.0ms

Algorithm

intervals

Results

44.0ms

268×

body

valid

simplify2.9s

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize30.0ms

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))))

rewrite121.0ms

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:

30.0ms	(* z (- t a))
19.0ms	(+ y (* z (- b y)))
16.0ms	(+ (* x y) (* z (- t a)))
51.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* z (- t a))
43.0ms	(+ y (* z (- b y)))
67.0ms	(+ (* x y) (* z (- t a)))
466.0ms	(/ (+ (* 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

localize57.0ms

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))))

rewrite61.0ms

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:

31.0ms	(* z (- t a))
13.0ms	(/ 1 (/ (fma (- b y) z y) (fma y x (* z (- t a)))))
0.0ms	(fma y x (* z (- t a)))
10.0ms	(/ (fma (- b y) z y) (fma y x (* z (- t a))))

series2.3s

Counts

4 → 12

Calls

4 calls:

54.0ms	(* z (- t a))
1.9s	(/ 1 (/ (fma (- b y) z y) (fma y x (* z (- t a)))))
71.0ms	(fma y x (* z (- t a)))
268.0ms	(/ (fma (- b y) z y) (fma y x (* z (- t a))))

simplify2.6s

Counts

179 → 179

Iterations

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

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma y x (* z (- t a)))
0.3b	(/ 1 (fma (- b y) z y))
25.4b	(* (/ 1 (fma (- b y) z y)) (fma y x (* z (- t a))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

44.0ms	(* z (- t a))
0.0ms	(fma y x (* z (- t a)))
8.0ms	(/ 1 (fma (- b y) z y))
11.0ms	(* (/ 1 (fma (- b y) z y)) (fma y x (* z (- t a))))

series2.1s

Counts

4 → 12

Calls

4 calls:

69.0ms	(* z (- t a))
99.0ms	(fma y x (* z (- t a)))
179.0ms	(/ 1 (fma (- b y) z y))
1.7s	(* (/ 1 (fma (- b y) z y)) (fma y x (* z (- t a))))

simplify2.9s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
3	3150
2	1032
1	468
0	212

prune813.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t a))
0.6b	(cbrt (- t a))
0.6b	(cbrt (- t a))
25.4b	(* (/ 1 (fma (- b y) z y)) (fma y x (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
15×	`cbrt-prod` `add-cube-cbrt`
13×	`associate-l` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `associate-r` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`div-exp` `cbrt-unprod` `fma-udef`
1×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `distribute-lft-in` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

3.0ms	(cbrt (- t a))
3.0ms	(cbrt (- t a))
3.0ms	(cbrt (- t a))
10.0ms	(* (/ 1 (fma (- b y) z y)) (fma y x (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt (- t a))
222.0ms	(cbrt (- t a))
179.0ms	(cbrt (- t a))
1.5s	(* (/ 1 (fma (- b y) z y)) (fma y x (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))))

simplify2.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
3	2566
2	878
1	350
0	158

prune662.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 9.7b

regimes781.0ms

Accuracy

-7.3% (11.0b remaining)

Error of 19.8b against oracle of 8.8b and baseline of 19.0b

bsearch272.0ms

Steps

Iters	Range		Point
7	4.5781043118532736e+282	1.8856943516558285e+284	1.854921660081858e+284
7	2.0610900308232754e+206	8.313708380325553e+207	2.3187126403961105e+207
10	3.056103735942779e-289	4.513537496159142e-272	6.721570574179068e-285
8	-1.916146495964301e-228	-7.6792701106166946e-233	-7.79363361577941e-233

simplify10.0ms

Iterations

Iter	Nodes
done	40
1	40
0	31

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.4s

8411×

body

valid