Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

272×

body

valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	66	15
4	97	15
5	131	15
6	164	15
7	240	15
8	473	15
9	1023	15
10	3735	15
done	5000	15

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.0b	(* z (- t a))
0.8b	(fma x y (* z (- t a)))
18.8b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`sub-neg` `associate-*r/` `fma-udef`
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 → 95

Calls

4 calls:

0.0ms	(fma z (- b y) y)
13.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
3.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series473.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(fma z (- b y) y)
38.0ms	(* z (- t a))
55.0ms	(fma x y (* z (- t a)))
353.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify3.4s

Counts

107 → 107

Iterations

Useful iterations: 3 (688.0ms)

Iter	Nodes	Cost
0	171	1678
1	316	1491
2	1086	1265
3	4478	1241
done	5000	1241

prune378.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 18.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.6b	(/ 1 (fma z (- b y) y))
0.8b	(fma x y (* z (- t a)))
18.4b	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

rewrite29.0ms

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×	`associate-r` `prod-diff`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
6×	`associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`flip3--` `pow-flip` `frac-2neg` `clear-num` `un-div-inv` `flip--` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 127

Calls

4 calls:

12.0ms	(* z (- t a))
2.0ms	(/ 1 (fma z (- b y) y))
0.0ms	(fma x y (* z (- t a)))
9.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* z (- t a))
72.0ms	(/ 1 (fma z (- b y) y))
59.0ms	(fma x y (* z (- t a)))
398.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

simplify1.3s

Counts

139 → 139

Iterations

Useful iterations: 2 (155.0ms)

Iter	Nodes	Cost
0	200	2133
1	405	1846
2	1401	1532
done	5001	1532

prune400.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 18.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.8b	(fma x y (* z (- t a)))
18.8b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite28.0ms

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×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`sub-neg` `rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num`
1×	`flip3--` `pow-flip` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 163

Calls

4 calls:

13.0ms	(* z (- t a))
6.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series808.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* z (- t a))
574.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
62.0ms	(fma x y (* z (- t a)))
127.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify1.5s

Counts

175 → 175

Iterations

Useful iterations: 2 (232.0ms)

Iter	Nodes	Cost
0	264	3896
1	536	3551
2	1903	3100
done	5002	3100

prune498.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 11.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t a))
0.5b	(cbrt (- t a))
0.8b	(fma x y (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a))))
18.8b	(/ (fma z (- b y) y) (fma x y (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
10×	`cbrt-prod`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `cbrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 73

Calls

4 calls:

2.0ms	(cbrt (- t a))
2.0ms	(cbrt (- t a))
0.0ms	(fma x y (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a))))
3.0ms	(/ (fma z (- b y) y) (fma x y (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(cbrt (- t a))
196.0ms	(cbrt (- t a))
67.0ms	(fma x y (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a))))
129.0ms	(/ (fma z (- b y) y) (fma x y (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))))

simplify1.1s

Counts

85 → 85

Iterations

Useful iterations: 3 (307.0ms)

Iter	Nodes	Cost
0	138	1840
1	269	1817
2	691	1267
3	2371	1092
done	5000	1092

prune363.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.4b

regimes419.0ms

Accuracy

15.9% (10.3b remaining)

Error of 20.8b against oracle of 10.6b and baseline of 22.8b

bsearch12.0ms

Steps

Iters	Range		Point
2	-3.330490411506177e+170	-2.8461895492187706e+170	-2.906727157004697e+170

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	19	26
done	19	26

end0.0ms

sample659.0ms

Algorithm

intervals

Results

355.0ms

8418×

body

valid