Details

sample156.0ms

Algorithm

intervals

Results

21.0ms	37×	body	1280	valid
16.0ms	45×	body	640	valid
13.0ms	146×	body	80	valid
4.0ms	15×	body	320	valid
2.0ms	13×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	42	14
6	44	14
done	44	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	(fma (tan x) (tan x) 1.0)
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.2b	(* (tan x) (tan x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
8.0ms	(- 1.0 (* (tan x) (tan x)))
16.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
36.0ms	(* (tan x) (tan x))

series262.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(fma (tan x) (tan x) 1.0)
38.0ms	(- 1.0 (* (tan x) (tan x)))
130.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
46.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

109 → 109

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	155	1557
1	330	1462
2	893	1345
3	2809	1320
done	5000	1314

prune468.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
10.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
1.0ms	(fma (- (tan x)) (tan x) 1.0)

series421.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(fma (tan x) (tan x) 1.0)
259.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
82.0ms	(fma (- (tan x)) (tan x) 1.0)

simplify2.1s

Counts

58 → 58

Iterations

Useful iterations: 3 (238.0ms)

Iter	Nodes	Cost
0	87	978
1	160	967
2	377	883
3	984	882
4	3063	882
done	5001	882

prune262.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
0.3b	(log1p (/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0)))
0.3b	(fma (- (tan x)) (tan x) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`fma-udef`
1×	`cbrt-undiv` `log1p-udef` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `div-inv`

Counts

4 → 60

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
5.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
0.0ms	(log1p (/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0)))
0.0ms	(fma (- (tan x)) (tan x) 1.0)

series783.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma (tan x) (tan x) 1.0)
228.0ms	(/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0))
389.0ms	(log1p (/ (fma (- (tan x)) (tan x) 1.0) (fma (tan x) (tan x) 1.0)))
88.0ms	(fma (- (tan x)) (tan x) 1.0)

simplify3.1s

Counts

72 → 72

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	114	1290
1	218	1274
2	533	1133
3	1436	1126
4	4747	1124
done	5000	1123

prune406.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 91

Calls

4 calls:

11.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
1.0ms	(fma (tan x) (tan x) 1.0)
34.0ms	(* (fma (- (tan x)) (tan x) 1.0) (/ 1 (fma (tan x) (tan x) 1.0)))
1.0ms	(fma (- (tan x)) (tan x) 1.0)

series915.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
484.0ms	(fma (tan x) (tan x) 1.0)
205.0ms	(* (fma (- (tan x)) (tan x) 1.0) (/ 1 (fma (tan x) (tan x) 1.0)))
88.0ms	(fma (- (tan x)) (tan x) 1.0)

simplify2.0s

Counts

103 → 103

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	131	1581
1	270	1438
2	665	1278
3	2035	1278
done	5000	1278

prune352.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes137.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	18
done	11	18

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1269×	body	640	valid
1.3s	1460×	body	1280	valid
898.0ms	4344×	body	80	valid
228.0ms	601×	body	320	valid
85.0ms	326×	body	160	valid