Details

sample453.0ms

Algorithm

intervals

Results

142.0ms	42×	body	2560	valid
115.0ms	86×	body	1280	valid
102.0ms	64×	body	640	valid
20.0ms	36×	body	320	valid
4.0ms	17×	body	160	valid
1.0ms	11×	body	80	valid

simplify248.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize39.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 1.0 (cos x))

rewrite57.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

37.0ms	(/ (- 1.0 (cos x)) (sin x))
14.0ms	(- 1.0 (cos x))

series128.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(/ (- 1.0 (cos x)) (sin x))
35.0ms	(- 1.0 (cos x))

simplify8.8s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
3	2309
2	767
1	308
0	134

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize97.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite419.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 177

Calls

3 calls:

292.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
50.0ms	(/ (sin x) (- 1.0 (cos x)))
29.0ms	(- 1.0 (cos x))

series401.0ms

Counts

3 → 9

Calls

3 calls:

248.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
94.0ms	(/ (sin x) (- 1.0 (cos x)))
44.0ms	(- 1.0 (cos x))

simplify14.7s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
3	4908
2	1543
1	650
0	269

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.4b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.7b	(- 1.0 (cos x))

rewrite156.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
44.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
47.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
15.0ms	(- 1.0 (cos x))

series371.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (- 1.0 (cos x)) (sin x))
160.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
93.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
45.0ms	(- 1.0 (cos x))

simplify5.6s

Counts

144 → 144

Iterations

Iter	Nodes
done	5001
3	2468
2	877
1	387
0	195

prune2.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x))) (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)))
0.3b	(* (cos x) (cos x))
0.6b	(+ (cos x) 1.0)
1.5b	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`difference-cubes` `cube-unmult` `pow3`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `swap-sqr` `associate-r` `associate-l` `associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `sqr-cos` `frac-2neg` `flip3-+` `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` `flip-+` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

165.0ms	(/ (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x))) (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)))
23.0ms	(* (cos x) (cos x))
15.0ms	(+ (cos x) 1.0)
68.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

series692.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(/ (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x))) (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)))
30.0ms	(* (cos x) (cos x))
19.0ms	(+ (cos x) 1.0)
397.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

simplify13.0s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
3	4717
2	1402
1	474
0	188

prune2.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.2b

regimes806.0ms

Accuracy

98.5% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.0b

bsearch4.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample27.3s

Algorithm

intervals

Results

9.9s	1604×	body	2560	valid
7.5s	2727×	body	1280	valid
6.6s	1853×	body	640	valid
2.6s	949×	body	320	valid
151.0ms	492×	body	160	valid
77.0ms	375×	body	80	valid