Details

sample92.0ms

Algorithm

intervals

Results

39.0ms	51×	body	2560	valid
12.0ms	35×	body	1280	valid
11.0ms	42×	body	640	valid
7.0ms	36×	body	320	valid
7.0ms	77×	body	80	valid
2.0ms	15×	body	160	valid

simplify28.0ms

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: 29.4b

localize19.0ms

Local error

Found 2 expressions with local error:

1.4b	(- 1.0 (cos x))
15.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite52.0ms

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))
21.0ms	(/ (- 1.0 (cos x)) (* x x))

series100.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
80.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.5s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	4103
2	936
1	290
0	116

prune297.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.4b	(- 1.0 (cos x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 165

Calls

3 calls:

27.0ms	(/ (/ (- 1.0 (cos x)) x) x)
14.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series166.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (/ (- 1.0 (cos x)) x) x)
60.0ms	(/ (- 1.0 (cos x)) x)
37.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

174 → 174

Iterations

Iter	Nodes
done	5003
2	1582
1	604
0	259

prune869.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (+ 1.0 (cos x)) (cos x) (* 1.0 1.0)) x))
0.4b	(pow (cos x) 3)
0.5b	(+ 1.0 (cos x))
1.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite143.0ms

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:

92.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (+ 1.0 (cos x)) (cos x) (* 1.0 1.0)) x))
3.0ms	(pow (cos x) 3)
5.0ms	(+ 1.0 (cos x))
31.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series372.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma (+ 1.0 (cos x)) (cos x) (* 1.0 1.0)) x))
43.0ms	(pow (cos x) 3)
14.0ms	(+ 1.0 (cos x))
70.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.2s

Counts

316 → 316

Iterations

Iter	Nodes
done	5024
2	2541
1	853
0	337

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.5b	(+ 1.0 (cos x))
1.2b	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))
1.3b	(log (exp (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

14.0ms	(* (cos x) (cos x))
5.0ms	(+ 1.0 (cos x))
33.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))
126.0ms	(log (exp (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (cos x) (cos x))
20.0ms	(+ 1.0 (cos x))
70.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))
67.0ms	(log (exp (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))))

simplify2.9s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
3	3483
2	1136
1	362
0	154

prune539.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes153.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.5b

bsearch103.0ms

Steps

Iters	Range		Point
8	0.0004390994911134099	0.778402845272117	0.03641414739962237
9	-0.1501579911863904	-8.136897775944376e-09	-0.031614486696612494

simplify15.0ms

Iterations

Iter	Nodes
done	48
1	48
0	40

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	1552×	body	2560	valid
947.0ms	1275×	body	1280	valid
420.0ms	1411×	body	640	valid
187.0ms	2308×	body	80	valid
180.0ms	956×	body	320	valid
68.0ms	498×	body	160	valid