Details

sample267.0ms

Algorithm

intervals

Results

118.0ms	57×	body	2560	valid
82.0ms	85×	body	1280	valid
30.0ms	66×	body	640	valid
8.0ms	28×	body	320	valid
3.0ms	14×	body	160	valid
2.0ms	6×	body	80	valid

simplify24.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize32.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.6b	(- 1.0 (cos x))

rewrite64.0ms

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--` `insert-posit16` `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 → 70

Calls

2 calls:

48.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(- 1.0 (cos x))

series111.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(/ (- 1.0 (cos x)) (sin x))
26.0ms	(- 1.0 (cos x))

simplify3.9s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	2324
2	768
1	310
0	136

prune763.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/240 (pow x 5) (* x (fma (* x 1/24) x 1/2)))
0.0b	(* x (fma (* x 1/24) x 1/2))
0.0b	(fma (* x 1/24) x 1/2)
0.4b	(* x 1/24)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 66

Calls

4 calls:

2.0ms	(fma 1/240 (pow x 5) (* x (fma (* x 1/24) x 1/2)))
19.0ms	(* x (fma (* x 1/24) x 1/2))
2.0ms	(fma (* x 1/24) x 1/2)
19.0ms	(* x 1/24)

series373.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(fma 1/240 (pow x 5) (* x (fma (* x 1/24) x 1/2)))
135.0ms	(* x (fma (* x 1/24) x 1/2))
101.0ms	(fma (* x 1/24) x 1/2)
33.0ms	(* x 1/24)

simplify4.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	5005
3	2116
2	472
1	189
0	94

prune911.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/240 (pow x 5) (+ (* (* (* x 1/24) x) x) (* 1/2 x)))
0.1b	(* (* (* x 1/24) x) x)
0.1b	(* (* x 1/24) x)
0.4b	(* x 1/24)

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-r`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

1.0ms	(fma 1/240 (pow x 5) (+ (* (* (* x 1/24) x) x) (* 1/2 x)))
112.0ms	(* (* (* x 1/24) x) x)
37.0ms	(* (* x 1/24) x)
10.0ms	(* x 1/24)

series238.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(fma 1/240 (pow x 5) (+ (* (* (* x 1/24) x) x) (* 1/2 x)))
71.0ms	(* (* (* x 1/24) x) x)
59.0ms	(* (* x 1/24) x)
19.0ms	(* x 1/24)

simplify11.5s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	4883
2	852
1	250
0	99

prune925.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.1b	(/ (sin x) (- 1.0 (cos x)))
2.6b	(- 1.0 (cos x))

rewrite140.0ms

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--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

3 → 180

Calls

3 calls:

53.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
40.0ms	(/ (sin x) (- 1.0 (cos x)))
11.0ms	(- 1.0 (cos x))

series195.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
79.0ms	(/ (sin x) (- 1.0 (cos x)))
43.0ms	(- 1.0 (cos x))

simplify7.0s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
3	4931
2	1796
1	649
0	272

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes461.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 32.1b

bsearch167.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	0.023709696647847237
10	-26711381.42537418	-6.803810524357175e-07	-0.022581149079332608

simplify23.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.5s	1603×	body	2560	valid
3.1s	2740×	body	1280	valid
1.0s	1901×	body	640	valid
421.0ms	934×	body	320	valid
96.0ms	465×	body	160	valid
76.0ms	356×	body	80	valid
8.0ms	1×	body	5120	valid