Details

sample214.0ms

Algorithm

intervals

Results

86.0ms	50×	body	1280	valid
22.0ms	42×	body	640	valid
15.0ms	135×	body	80	valid
7.0ms	20×	body	320	valid
5.0ms	9×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	43	14
6	45	14
done	45	14

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

20.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
17.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

series283.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
41.0ms	(- 1.0 (* (tan x) (tan x)))
36.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

131 → 131

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	151	1789
1	377	1658
2	1700	1455
done	5000	1439

prune481.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
0.1b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
89×	`add-sqr-sqrt`
70×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-/r*`
19×	`add-exp-log`
17×	`difference-of-squares`
13×	`add-cbrt-cube`
12×	`pow1`
11×	`associate-/r/`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*` `add-log-exp`
4×	`tan-quot` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow2` `frac-times` `sub-neg` `pow-flip` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 184

Calls

4 calls:

20.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
41.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
12.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))

series456.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
160.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
68.0ms	(- 1.0 (* (tan x) (tan x)))
41.0ms	(* (tan x) (tan x))

simplify2.1s

Counts

196 → 196

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	281	4304
1	687	3941
2	3627	3711
done	5000	3692

prune638.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(/ (fma (tan x) (tan x) 1.0) (+ (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) (* (tan x) (+ (- (tan x)) (tan x)))))
0.1b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (+ (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) (* (tan x) (+ (- (tan x)) (tan x))))))
0.3b	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
18.0ms	(/ (fma (tan x) (tan x) 1.0) (+ (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) (* (tan x) (+ (- (tan x)) (tan x)))))
30.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (+ (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) (* (tan x) (+ (- (tan x)) (tan x))))))
1.0ms	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))

series566.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(fma (tan x) (tan x) 1.0)
215.0ms	(/ (fma (tan x) (tan x) 1.0) (+ (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) (* (tan x) (+ (- (tan x)) (tan x)))))
166.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (+ (fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3)) (* (tan x) (+ (- (tan x)) (tan x))))))
116.0ms	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))

simplify2.4s

Counts

149 → 149

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	226	6037
1	550	5161
2	2869	4576
done	5001	3718

prune717.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma (tan x) 0 (fma (- (tan x)) (tan x) 1.0)) (fma (tan x) 0 (fma (- (tan x)) (tan x) 1.0)))
0.3b	(fma (- (tan x)) (tan x) 1.0)
0.3b	(fma (- (tan x)) (tan x) 1.0)
0.3b	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
5×	`fma-udef`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

8.0ms	(* (fma (tan x) 0 (fma (- (tan x)) (tan x) 1.0)) (fma (tan x) 0 (fma (- (tan x)) (tan x) 1.0)))
0.0ms	(fma (- (tan x)) (tan x) 1.0)
0.0ms	(fma (- (tan x)) (tan x) 1.0)
0.0ms	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))

series413.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (fma (tan x) 0 (fma (- (tan x)) (tan x) 1.0)) (fma (tan x) 0 (fma (- (tan x)) (tan x) 1.0)))
82.0ms	(fma (- (tan x)) (tan x) 1.0)
104.0ms	(fma (- (tan x)) (tan x) 1.0)
76.0ms	(fma (- (tan x)) (tan x) (pow (cbrt 1.0) 3))

simplify757.0ms

Counts

71 → 71

Iterations

Useful iterations: done (754.0ms)

Iter	Nodes	Cost
0	84	1313
1	175	1043
2	816	778
done	5002	763

prune443.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes145.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	51
1	20	51
done	20	51

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.4s	1544×	body	1280	valid
1.3s	1255×	body	640	valid
668.0ms	4290×	body	80	valid
495.0ms	287×	body	160	valid
368.0ms	624×	body	320	valid