Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	50×	body	2560	valid
10.0ms	45×	body	1280	valid
6.0ms	45×	body	640	valid
3.0ms	73×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	20×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	29	8
done	29	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize9.0ms

Local error

Found 2 expressions with local error:

3.4b	(- 1.0 (cos x))
15.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
10.0ms	(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.9s

Counts

64 → 64

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	116	808
1	272	678
2	845	566
3	3719	526
done	5000	525

prune132.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.4b	(- 1.0 (cos x))
3.4b	(- 1.0 (cos x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
156×	`times-frac`
104×	`sqrt-prod`
103×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `prod-diff` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
6×	`fma-neg`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 238

Calls

4 calls:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
43.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series173.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (sqrt (- 1.0 (cos x))) x)
42.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
22.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

250 → 250

Iterations

Useful iterations: 2 (541.0ms)

Iter	Nodes	Cost
0	261	4851
1	723	3988
2	2597	3318
done	5000	3318

prune445.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ (/ (- 1.0 (cos x)) x) x)))
0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
3.4b	(- 1.0 (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 176

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (/ (- 1.0 (cos x)) x) x)))
12.0ms	(/ (/ (- 1.0 (cos x)) x) x)
9.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series399.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(expm1 (log1p (/ (/ (- 1.0 (cos x)) x) x)))
47.0ms	(/ (/ (- 1.0 (cos x)) x) x)
43.0ms	(/ (- 1.0 (cos x)) x)
23.0ms	(- 1.0 (cos x))

simplify773.0ms

Counts

188 → 188

Iterations

Useful iterations: 2 (349.0ms)

Iter	Nodes	Cost
0	270	2748
1	603	2504
2	1586	2313
done	5000	2313

prune408.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (+ 1.0 (cos x)))
0.2b	(* (cos x) (cos x))
0.4b	(+ 1.0 (cos x))
3.6b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
16×	`times-frac`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`distribute-lft-out` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`fma-def` `swap-sqr` `associate-r` `associate-l`
2×	`sqr-cos` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `associate--r+` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

11.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (+ 1.0 (cos x)))
4.0ms	(* (cos x) (cos x))
3.0ms	(+ 1.0 (cos x))
3.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (+ 1.0 (cos x)))
17.0ms	(* (cos x) (cos x))
14.0ms	(+ 1.0 (cos x))
33.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify515.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (181.0ms)

Iter	Nodes	Cost
0	168	1624
1	395	1399
2	1290	1293
done	5002	1293

prune315.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes45.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 30.7b

bsearch69.0ms

Steps

Iters	Range		Point
9	6.379368274952145e-05	25.411711264148785	0.030256823677706827
10	-155084744.97222546	-0.0009113054925467739	-0.029841445064018916

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	24	40
1	28	31
done	28	31

end0.0ms

sample1.6s

Algorithm

intervals

Results

765.0ms	1655×	body	2560	valid
270.0ms	1208×	body	1280	valid
207.0ms	1464×	body	640	valid
101.0ms	951×	body	320	valid
68.0ms	2222×	body	80	valid
35.0ms	500×	body	160	valid