Details

sample68.0ms

Algorithm

intervals

Results

51.0ms

719×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2849
6	771
5	316
4	187
3	84
2	39
1	18
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (cosh x) (/ y x))
0.0b	(cosh x)
3.8b	(/ (* (cosh x) (/ y x)) z)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`add-cbrt-cube` `add-exp-log`
13×	`-un-lft-identity` `times-frac` `associate-r*` `add-cube-cbrt`
5×	`pow1` `cbrt-undiv` `cosh-def` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `associate-l*` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`frac-times` `associate-l/` `associate-r/` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l`

Counts

3 → 77

Calls

3 calls:

14.0ms	(* (cosh x) (/ y x))
3.0ms	(cosh x)
23.0ms	(/ (* (cosh x) (/ y x)) z)

series311.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(* (cosh x) (/ y x))
51.0ms	(cosh x)
138.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5006
2	1389
1	389
0	159

prune537.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/2 (exp x) (/ 1/2 (exp x)))
0.0b	(/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z)
0.0b	(/ 1/2 (exp x))
3.8b	(* (/ y x) (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube`
19×	`add-exp-log`
13×	`associate-r` `associate-l`
6×	`pow1` `cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

4 → 124

Calls

4 calls:

0.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
8.0ms	(/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z)
16.0ms	(/ 1/2 (exp x))
24.0ms	(* (/ y x) (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z))

series335.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
94.0ms	(/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z)
10.0ms	(/ 1/2 (exp x))
156.0ms	(* (/ y x) (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z))

simplify2.5s

Counts

136 → 136

Iterations

Iter	Nodes
done	5003
2	2038
1	528
0	215

prune836.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ z (fma 1/2 (exp x) (/ 1/2 (exp x))))
0.0b	(fma 1/2 (exp x) (/ 1/2 (exp x)))
0.0b	(/ 1/2 (exp x))
3.7b	(/ (/ y x) (/ z (fma 1/2 (exp x) (/ 1/2 (exp x)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

439×	`times-frac`
216×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
31×	`div-inv`
20×	`add-cbrt-cube`
19×	`associate-/r` `add-exp-log` `associate-/l`
10×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`associate-/r/` `fma-udef` `associate-/l/`

Counts

4 → 289

Calls

4 calls:

9.0ms	(/ z (fma 1/2 (exp x) (/ 1/2 (exp x))))
0.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
11.0ms	(/ 1/2 (exp x))
19.0ms	(/ (/ y x) (/ z (fma 1/2 (exp x) (/ 1/2 (exp x)))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ z (fma 1/2 (exp x) (/ 1/2 (exp x))))
58.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
15.0ms	(/ 1/2 (exp x))
184.0ms	(/ (/ y x) (/ z (fma 1/2 (exp x) (/ 1/2 (exp x)))))

simplify1.7s

Counts

301 → 301

Iterations

Iter	Nodes
done	5000
1	1565
0	526

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ z (fma 1/2 (exp x) (/ 1/2 (exp x)))))
0.0b	(fma 1/2 (exp x) (/ 1/2 (exp x)))
0.0b	(/ 1/2 (exp x))
3.8b	(* (/ y x) (/ 1 (/ z (fma 1/2 (exp x) (/ 1/2 (exp x))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

176×	`times-frac`
129×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
96×	`add-cube-cbrt`
61×	`add-exp-log`
44×	`associate-r`
32×	`add-cbrt-cube`
29×	`div-exp`
16×	`associate-/r*`
14×	`prod-exp`
13×	`cbrt-undiv` `associate-l`
11×	`div-inv`
10×	`unswap-sqr`
7×	`pow1`
6×	`rec-exp` `1-exp` `cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 223

Calls

4 calls:

13.0ms	(/ 1 (/ z (fma 1/2 (exp x) (/ 1/2 (exp x)))))
0.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
17.0ms	(/ 1/2 (exp x))
38.0ms	(* (/ y x) (/ 1 (/ z (fma 1/2 (exp x) (/ 1/2 (exp x))))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ 1 (/ z (fma 1/2 (exp x) (/ 1/2 (exp x)))))
62.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
10.0ms	(/ 1/2 (exp x))
158.0ms	(* (/ y x) (/ 1 (/ z (fma 1/2 (exp x) (/ 1/2 (exp x))))))

simplify2.0s

Counts

235 → 235

Iterations

Iter	Nodes
done	5008
2	2938
1	1005
0	349

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes202.0ms

Accuracy

94.1% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 7.5b

bsearch129.0ms

Steps

Iters	Range		Point
4	1.766624877482737e-20	2.4836067088222448e-20	2.0130873820056925e-20
7	-3.197232192274342e-65	-7.463908164699712e-67	-3.1569808277222708e-65

simplify9.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.3s

21882×

body

valid