Details

sample161.0ms

Algorithm

intervals

Results

77.0ms	57×	body	2560	valid
43.0ms	82×	body	1280	valid
16.0ms	58×	body	640	valid
13.0ms	38×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	8×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.3b	(- 1.0 (cos x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 68

Calls

2 calls:

50.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(- 1.0 (cos x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(/ (- 1.0 (cos x)) (sin x))
27.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

74 → 74

Iterations

Iter	Nodes
done	5002
3	2334
2	774
1	308
0	134

prune412.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma (+ (cos x) 1.0) (cos x) (* 1.0 1.0))))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite185.0ms

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:

85.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma (+ (cos x) 1.0) (cos x) (* 1.0 1.0))))
6.0ms	(pow (cos x) 3)
11.0ms	(+ (cos x) 1.0)
61.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series377.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma (+ (cos x) 1.0) (cos x) (* 1.0 1.0))))
52.0ms	(pow (cos x) 3)
19.0ms	(+ (cos x) 1.0)
73.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.1s

Counts

316 → 316

Iterations

Iter	Nodes
done	5061
2	2658
1	862
0	340

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
1.5b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
222×	`add-sqr-sqrt`
218×	`*-un-lft-identity`
210×	`add-cube-cbrt`
169×	`prod-diff`
31×	`div-inv`
13×	`fma-neg`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

3 → 265

Calls

3 calls:

14.0ms	(/ 1.0 (sin x))
13.0ms	(/ (cos x) (sin x))
42.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series188.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ 1.0 (sin x))
25.0ms	(/ (cos x) (sin x))
137.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify2.2s

Counts

274 → 274

Iterations

Iter	Nodes
done	5002
2	2009
1	842
0	371

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos x) (cos x)) (* (cos x) (cos x)))
0.3b	(cbrt (* (* (* (cos x) (cos x)) (cos x)) (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (cos x) (cos x)))))
0.4b	(+ (cos x) 1.0)
1.2b	(- (pow 1.0 3) (cbrt (* (* (* (cos x) (cos x)) (cos x)) (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (cos x) (cos x))))))

rewrite924.0ms

Algorithm

rewrite-expression-head

Rules

115×	`pow1`
48×	`prod-diff`
39×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `cos-mult` `pow-prod-up`
32×	`add-cube-cbrt`
24×	`pow-prod-down`
22×	`pow-sqr`
20×	`associate-*l/`
18×	`frac-times` `pow-plus`
16×	`unpow-prod-down` `add-cbrt-cube` `cube-prod` `add-exp-log`
15×	`cbrt-div`
14×	`associate-*r/`
13×	`cbrt-prod` `pow2`
12×	`fma-neg`
8×	`prod-exp` `cbrt-unprod` `add-log-exp`
6×	`sqr-pow`
5×	`cube-mult` `unpow3`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-def`
2×	`sqr-cos` `pow3`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `flip3--` `pow1/3` `diff-log` `swap-sqr` `associate-r` `associate-l` `*-commutative` `rem-cbrt-cube` `flip-+` `flip--` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 193

Calls

4 calls:

45.0ms	(* (* (cos x) (cos x)) (* (cos x) (cos x)))
829.0ms	(cbrt (* (* (* (cos x) (cos x)) (cos x)) (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (cos x) (cos x)))))
11.0ms	(+ (cos x) 1.0)
22.0ms	(- (pow 1.0 3) (cbrt (* (* (* (cos x) (cos x)) (cos x)) (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (cos x) (cos x))))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* (cos x) (cos x)) (* (cos x) (cos x)))
44.0ms	(cbrt (* (* (* (cos x) (cos x)) (cos x)) (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (cos x) (cos x)))))
17.0ms	(+ (cos x) 1.0)
67.0ms	(- (pow 1.0 3) (cbrt (* (* (* (cos x) (cos x)) (cos x)) (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (cos x) (cos x))))))

simplify1.7s

Counts

205 → 205

Iterations

Iter	Nodes
done	5000
2	1762
1	687
0	262

prune732.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

regimes172.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.8b

bsearch160.0ms

Steps

Iters	Range		Point
11	3.4817375791661903e-26	573579.0075499975	0.02105783752125853
10	-84463.33967257517	-3.2432757514909933e-09	-0.02231715051571105

simplify9.0ms

Iterations

Iter	Nodes
done	45
1	45
0	36

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.1s	1642×	body	2560	valid
2.8s	2753×	body	1280	valid
949.0ms	1876×	body	640	valid
257.0ms	927×	body	320	valid
89.0ms	452×	body	160	valid
37.0ms	5×	body	5120	valid
37.0ms	345×	body	80	valid