Details

sample127.0ms

Algorithm

intervals

Results

50.0ms	40×	body	2560	valid
28.0ms	52×	body	1280	valid
14.0ms	40×	body	640	valid
9.0ms	37×	body	320	valid
5.0ms	67×	body	80	valid
3.0ms	20×	body	160	valid

simplify25.0ms

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: 30.3b

localize19.0ms

Local error

Found 2 expressions with local error:

1.7b	(- 1.0 (cos x))
14.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite51.0ms

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` `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 → 58

Calls

2 calls:

11.0ms	(- 1.0 (cos x))
37.0ms	(/ (- 1.0 (cos x)) (* x x))

series153.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- 1.0 (cos x))
116.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
2	1734
1	301
0	116

prune271.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.7b	(- 1.0 (cos x))

rewrite94.0ms

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` `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 → 132

Calls

3 calls:

60.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
14.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series151.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
63.0ms	(/ (- 1.0 (cos x)) x)
36.0ms	(- 1.0 (cos x))

simplify3.5s

Counts

141 → 141

Iterations

Iter	Nodes
done	5001
2	3865
1	617
0	219

prune637.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
0.1b	(/ 1 (/ x (- 1.0 (cos x))))
0.2b	(/ x (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

283×	`times-frac`
234×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
135×	`add-cube-cbrt`
100×	`add-exp-log`
68×	`associate-r`
50×	`div-exp`
32×	`add-cbrt-cube`
28×	`prod-exp`
26×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
18×	`associate-/r/`
17×	`rec-exp` `1-exp`
15×	`unswap-sqr`
13×	`cbrt-undiv` `associate-l`
11×	`div-inv`
9×	`pow1` `flip3--` `prod-diff` `flip--`
6×	`cbrt-unprod` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `pow-prod-down` `pow-flip` `inv-pow`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `sub-neg` `diff-log` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Counts

4 → 324

Calls

4 calls:

72.0ms	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
31.0ms	(/ 1 (/ x (- 1.0 (cos x))))
14.0ms	(/ x (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series225.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (/ 1 x) (/ 1 (/ x (- 1.0 (cos x)))))
75.0ms	(/ 1 (/ x (- 1.0 (cos x))))
64.0ms	(/ x (- 1.0 (cos x)))
21.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

336 → 336

Iterations

Iter	Nodes
done	5000
1	1349
0	418

prune1.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.3b	(* (cos x) (cos x))
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.5b	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sqr-cos`
2×	`pow2` `pow-plus` `pow3` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`difference-cubes` `+-commutative` `associate-+l+` `sum-log` `sub-neg` `fma-def` `flip3-+` `distribute-rgt-out` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip-+` `flip--`

Counts

4 → 91

Calls

4 calls:

8.0ms	(* (cos x) (cos x))
8.0ms	(* (cos x) (cos x))
14.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
44.0ms	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (cos x) (cos x))
24.0ms	(* (cos x) (cos x))
50.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
62.0ms	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))

simplify2.9s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2793
1	377
0	126

prune477.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes146.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.7b

bsearch111.0ms

Steps

Iters	Range		Point
7	0.00012587414935880383	0.030359728269424062	0.02891102314655495
11	-14746478108.679678	-8.433739504313006e-14	-0.023093105424753346

simplify9.0ms

Iterations

Iter	Nodes
done	50
1	50
0	38

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	1570×	body	2560	valid
748.0ms	1477×	body	640	valid
623.0ms	1253×	body	1280	valid
167.0ms	967×	body	320	valid
167.0ms	2260×	body	80	valid
55.0ms	473×	body	160	valid