Details

sample159.0ms

Algorithm

intervals

Results

72.0ms	59×	body	2560	valid
22.0ms	49×	body	640	valid
22.0ms	33×	body	1280	valid
12.0ms	36×	body	320	valid
7.0ms	66×	body	80	valid
3.0ms	13×	body	160	valid

simplify136.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize55.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
15.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-cbrt-cube` `add-exp-log`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`expm1-log1p-u` `pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 60

Calls

2 calls:

28.0ms	(- 1.0 (cos x))
76.0ms	(/ (- 1.0 (cos x)) (* x x))

series127.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(- 1.0 (cos x))
96.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify6.4s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3754
2	888
1	294
0	118

prune645.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* x x) (* 1/720 (* x x)) 1/2)
0.8b	(* 1/720 (* x x))
11.6b	(fma (* x x) -1/24 (fma (* x x) (* 1/720 (* x x)) 1/2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`associate-r` `*-commutative` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

1.0ms	(fma (* x x) (* 1/720 (* x x)) 1/2)
44.0ms	(* 1/720 (* x x))
1.0ms	(fma (* x x) -1/24 (fma (* x x) (* 1/720 (* x x)) 1/2))

series304.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(fma (* x x) (* 1/720 (* x x)) 1/2)
51.0ms	(* 1/720 (* x x))
75.0ms	(fma (* x x) -1/24 (fma (* x x) (* 1/720 (* x x)) 1/2))

simplify4.2s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	1963
2	417
1	147
0	70

prune577.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize107.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.8b	(- 1.0 (cos x))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
46×	`times-frac`
36×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp` `prod-diff`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r*` `fma-neg` `insert-posit16` `log1p-expm1-u` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 135

Calls

3 calls:

110.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
44.0ms	(/ (- 1.0 (cos x)) x)
28.0ms	(- 1.0 (cos x))

series200.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
103.0ms	(/ (- 1.0 (cos x)) x)
25.0ms	(- 1.0 (cos x))

simplify4.0s

Counts

144 → 144

Iterations

Iter	Nodes
done	5002
2	1772
1	593
0	222

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize193.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x)))) (fma (+ 1.0 (cos x)) (cos x) (* 1.0 1.0)))
0.2b	(* (cos x) (cos x))
0.3b	(+ 1.0 (cos x))
1.7b	(- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x))))

rewrite363.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`difference-cubes` `cube-unmult` `pow3`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`sqr-cos` `associate-/r` `fma-def` `swap-sqr` `associate-r` `associate-l*`
2×	`flip3--` `flip--` `associate--r+` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `pow-plus` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

219.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x)))) (fma (+ 1.0 (cos x)) (cos x) (* 1.0 1.0)))
33.0ms	(* (cos x) (cos x))
15.0ms	(+ 1.0 (cos x))
90.0ms	(- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x))))

series532.0ms

Counts

4 → 12

Calls

4 calls:

355.0ms	(/ (- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x)))) (fma (+ 1.0 (cos x)) (cos x) (* 1.0 1.0)))
52.0ms	(* (cos x) (cos x))
24.0ms	(+ 1.0 (cos x))
100.0ms	(- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x))))

simplify8.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	4587
2	1430
1	499
0	195

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes196.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.3b

bsearch187.0ms

Steps

Iters	Range		Point
10	4.3052657707541446e-11	1.874259372897972	0.031731941663915054
8	-0.28008678268591264	-0.00018185218373056224	-0.02712486700916196

simplify48.0ms

Iterations

Iter	Nodes
done	59
1	59
0	47

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.7s	1535×	body	2560	valid
1.0s	1557×	body	640	valid
790.0ms	1240×	body	1280	valid
287.0ms	909×	body	320	valid
226.0ms	2260×	body	80	valid
117.0ms	499×	body	160	valid