Details

sample124.0ms

Algorithm

intervals

Results

59.0ms	48×	body	2560	valid
19.0ms	42×	body	1280	valid
17.0ms	52×	body	640	valid
6.0ms	27×	body	320	valid
4.0ms	68×	body	80	valid
3.0ms	19×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize17.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
15.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite32.0ms

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:

6.0ms	(- 1.0 (cos x))
24.0ms	(/ (- 1.0 (cos x)) (* x x))

series94.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
73.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
2	1734
1	301
0	116

prune310.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.1b	(- 1.0 (cos x))

rewrite92.0ms

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:

58.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
16.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series160.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
56.0ms	(/ (- 1.0 (cos x)) x)
38.0ms	(- 1.0 (cos x))

simplify3.1s

Counts

141 → 141

Iterations

Iter	Nodes
done	5001
2	3865
1	617
0	219

prune558.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)) x))
0.5b	(+ (cos x) 1.0)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
144×	`prod-diff`
117×	`*-un-lft-identity`
114×	`unpow-prod-down` `cube-prod`
85×	`add-cube-cbrt`
50×	`sqr-pow`
48×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
15×	`distribute-lft-out--`
12×	`fma-neg`
10×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow` `fma-def`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`pow-to-exp` `+-commutative` `clear-num` `associate-/r*` `sum-log` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 304

Calls

4 calls:

5.0ms	(pow (cos x) 3)
120.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)) x))
10.0ms	(+ (cos x) 1.0)
51.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series379.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (cos x) 3)
248.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)) x))
17.0ms	(+ (cos x) 1.0)
84.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify3.1s

Counts

316 → 316

Iterations

Iter	Nodes
done	5000
2	4578
1	869
0	339

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (cos x) 1.0))
0.7b	(cbrt (+ (cos x) 1.0))
0.7b	(cbrt (+ (cos x) 1.0))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
106×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
87×	`unpow-prod-down` `cube-prod`
82×	`add-cube-cbrt`
33×	`sqr-pow`
25×	`cube-mult` `unpow3`
16×	`difference-of-squares`
12×	`cbrt-prod` `fma-neg`
6×	`cbrt-div` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 240

Calls

4 calls:

4.0ms	(cbrt (+ (cos x) 1.0))
6.0ms	(cbrt (+ (cos x) 1.0))
4.0ms	(cbrt (+ (cos x) 1.0))
38.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series713.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (+ (cos x) 1.0))
223.0ms	(cbrt (+ (cos x) 1.0))
247.0ms	(cbrt (+ (cos x) 1.0))
52.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.3s

Counts

252 → 252

Iterations

Iter	Nodes
done	5000
2	2485
1	591
0	252

prune863.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes213.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch104.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.033302914266201536
8	-0.9341403346610884	-0.003292329160956242	-0.03305631426271166

simplify34.0ms

Iterations

Iter	Nodes
done	46
2	46
1	45
0	36

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.9s	1623×	body	2560	valid
584.0ms	1237×	body	1280	valid
424.0ms	1505×	body	640	valid
170.0ms	923×	body	320	valid
121.0ms	2205×	body	80	valid
71.0ms	507×	body	160	valid