Details

sample261.0ms

Algorithm

intervals

Results

108.0ms	56×	body	2560	valid
95.0ms	79×	body	1280	valid
25.0ms	58×	body	640	valid
11.0ms	38×	body	320	valid
4.0ms	17×	body	160	valid
1.0ms	8×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize19.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite25.0ms

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:

15.0ms	(/ (- 1.0 (cos x)) (sin x))
8.0ms	(- 1.0 (cos x))

series412.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
371.0ms	(- 1.0 (cos x))

simplify917.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune364.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/24 (pow x 3) (fma (pow x 5) 1/240 (* 1/2 x)))
0.0b	(fma (pow x 5) 1/240 (* 1/2 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 1/24 (pow x 3) (fma (pow x 5) 1/240 (* 1/2 x)))
0.0ms	(fma (pow x 5) 1/240 (* 1/2 x))

series304.0ms

Counts

2 → 6

Calls

2 calls:

100.0ms	(fma 1/24 (pow x 3) (fma (pow x 5) 1/240 (* 1/2 x)))
204.0ms	(fma (pow x 5) 1/240 (* 1/2 x))

simplify669.0ms

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
3	819
2	177
1	62
0	35

prune216.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.5b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.1b	(- 1.0 (cos x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

21.0ms	(/ (- 1.0 (cos x)) (sin x))
17.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
28.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
6.0ms	(- 1.0 (cos x))

series208.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (- 1.0 (cos x)) (sin x))
66.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
58.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
24.0ms	(- 1.0 (cos x))

simplify1.0s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1390
1	392
0	195

prune674.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (/ 1 (sin x)) (- 1.0 (cos x)))
2.1b	(- 1.0 (cos x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
38×	`add-cube-cbrt`
27×	`prod-diff`
20×	`times-frac`
16×	`add-exp-log`
13×	`associate-l`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-r` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `associate-/r` `sub-neg` `flip3--` `fma-neg` `log1p-expm1-u` `flip--` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*r/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`clear-num` `frac-2neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 126

Calls

3 calls:

7.0ms	(/ 1 (sin x))
42.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series78.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(/ 1 (sin x))
41.0ms	(* (/ 1 (sin x)) (- 1.0 (cos x)))
20.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	3723
1	541
0	204

prune419.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes261.0ms

Accuracy

98.2% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 32.2b

bsearch1.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	35
1	35
0	31

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.5s	1579×	body	2560	valid
2.7s	2757×	body	1280	valid
1.5s	1907×	body	640	valid
402.0ms	945×	body	320	valid
168.0ms	487×	body	160	valid
38.0ms	323×	body	80	valid
24.0ms	2×	body	5120	valid