Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	50×	body	2560	valid
9.0ms	45×	body	1280	valid
6.0ms	45×	body	640	valid
2.0ms	73×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	20×	body	160	valid

simplify16.0ms

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

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

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))

series63.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
42.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify427.0ms

Counts

64 → 64

Iterations

Useful iterations: done (425.0ms)

Iter	Nodes	Cost
0	116	808
1	285	686
2	966	566
done	5000	527

prune131.0ms

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))

rewrite68.0ms

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)
42.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series167.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (sqrt (- 1.0 (cos x))) x)
45.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

250 → 250

Iterations

Useful iterations: 2 (270.0ms)

Iter	Nodes	Cost
0	261	4851
1	740	4008
2	3201	3318
done	5001	3318

prune438.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (/ (- 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))

rewrite31.0ms

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` `log1p-udef` `diff-log` `log1p-expm1`

Counts

4 → 176

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (/ (- 1.0 (cos x)) x) x)))
11.0ms	(/ (/ (- 1.0 (cos x)) x) x)
9.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series658.0ms

Counts

4 → 12

Calls

4 calls:

547.0ms	(log1p (expm1 (/ (/ (- 1.0 (cos x)) x) x)))
45.0ms	(/ (/ (- 1.0 (cos x)) x) x)
42.0ms	(/ (- 1.0 (cos x)) x)
23.0ms	(- 1.0 (cos x))

simplify915.0ms

Counts

188 → 188

Iterations

Useful iterations: 2 (211.0ms)

Iter	Nodes	Cost
0	290	2827
1	671	2582
2	2417	2377
done	5000	2377

prune406.0ms

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) (pow (cos x) 2)) (+ 1.0 (cos x)))
0.2b	(pow (cos x) 2)
0.4b	(+ 1.0 (cos x))
3.6b	(- (* 1.0 1.0) (pow (cos x) 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
28×	`times-frac`
24×	`difference-of-squares`
22×	`add-cube-cbrt`
12×	`unpow-prod-down`
9×	`distribute-lft-out`
8×	`prod-diff` `unpow2` `add-log-exp` `sqr-pow`
7×	`add-exp-log` `associate-/l*`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-unpow` `fma-def`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 122

Calls

4 calls:

20.0ms	(/ (- (* 1.0 1.0) (pow (cos x) 2)) (+ 1.0 (cos x)))
1.0ms	(pow (cos x) 2)
3.0ms	(+ 1.0 (cos x))
6.0ms	(- (* 1.0 1.0) (pow (cos x) 2))

series125.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (- (* 1.0 1.0) (pow (cos x) 2)) (+ 1.0 (cos x)))
17.0ms	(pow (cos x) 2)
10.0ms	(+ 1.0 (cos x))
36.0ms	(- (* 1.0 1.0) (pow (cos x) 2))

simplify854.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (191.0ms)

Iter	Nodes	Cost
0	222	2120
1	526	1867
2	1871	1661
done	5001	1661

prune327.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch67.0ms

Steps

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

simplify3.0ms

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

745.0ms	1655×	body	2560	valid
262.0ms	1208×	body	1280	valid
211.0ms	1464×	body	640	valid
105.0ms	951×	body	320	valid
76.0ms	2222×	body	80	valid
35.0ms	500×	body	160	valid