Details

sample541.0ms

Algorithm

intervals

Results

247.0ms	55×	body	2560	valid
121.0ms	86×	body	1280	valid
47.0ms	57×	body	640	valid
24.0ms	36×	body	320	valid
6.0ms	14×	body	160	valid
2.0ms	8×	body	80	valid

simplify76.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (tan x))
1.1b	(- x (sin x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 113

Calls

3 calls:

18.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
14.0ms	(- x (sin x))

series264.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (- x (sin x)) (- x (tan x)))
82.0ms	(- x (tan x))
55.0ms	(- x (sin x))

simplify840.0ms

Counts

122 → 122

Iterations

Iter	Nodes
done	2000
2	1279
1	504
0	212

prune473.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) (* x x))
0.3b	(fma 27/2800 (* (* x x) (* x x)) 1/2)
16.1b	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 88

Calls

3 calls:

46.0ms	(* (* x x) (* x x))
0.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
1.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (* x x) (* x x))
158.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
93.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

simplify521.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	2022
2	665
1	202
0	79

prune242.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x))
0.3b	(fma (/ (sin x) (* (cos x) (cos x))) (/ (sin x) (* x x)) (/ (/ (sin x) (cos x)) x))
15.4b	(/ (sin x) (* x x))
15.4b	(/ (sin x) (* x x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 70

Calls

4 calls:

0.0ms	(fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x))
0.0ms	(fma (/ (sin x) (* (cos x) (cos x))) (/ (sin x) (* x x)) (/ (/ (sin x) (cos x)) x))
11.0ms	(/ (sin x) (* x x))
17.0ms	(/ (sin x) (* x x))

series575.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(fma (/ (sin x) (cos x)) (/ (sin x) (* x x)) (/ (sin x) x))
240.0ms	(fma (/ (sin x) (* (cos x) (cos x))) (/ (sin x) (* x x)) (/ (/ (sin x) (cos x)) x))
45.0ms	(/ (sin x) (* x x))
47.0ms	(/ (sin x) (* x x))

simplify653.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	2004
2	844
1	227
0	107

prune496.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.5b

bsearch202.0ms

Steps

Iters	Range		Point
11	0.0038666078177206752	9.350013159855062e+31	2.412135160853593
10	-121993772661.31783	-0.0015977726548224043	-4.773716110019835

simplify11.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample16.5s

Algorithm

intervals

Results

6.7s	1651×	body	2560	valid
4.9s	2716×	body	1280	valid
3.0s	1864×	body	640	valid
1.3s	986×	body	320	valid
287.0ms	442×	body	160	valid
82.0ms	341×	body	80	valid