Details

sample304.0ms

Algorithm

intervals

Results

23.0ms	49×	body	1280	valid
12.0ms	44×	body	640	valid
8.0ms	140×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify29.0ms

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	42	14
6	44	14
done	44	14

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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)
2.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
7.0ms	(* (tan x) (tan x))

series227.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma (tan x) (tan x) 1.0)
35.0ms	(- 1.0 (* (tan x) (tan x)))
110.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
41.0ms	(* (tan x) (tan x))

simplify500.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	155	1557
1	336	1462
2	1117	1345
done	5000	1345

prune261.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (cos x) 2)
4.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series72.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
18.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)

simplify1.2s

Counts

92 → 92

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	68	616
1	149	530
2	472	466
3	1509	466
done	5000	466

prune241.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.2b	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))
0.2b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))
0.2b	(* (tan x) (tan x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.0ms	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))
0.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))
5.0ms	(* (tan x) (tan x))

series655.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
291.0ms	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))
225.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))
35.0ms	(* (tan x) (tan x))

simplify494.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	174	1763
1	370	1670
2	1245	1471
done	5000	1471

prune270.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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:

2.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
4.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))

series273.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
103.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
105.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

196 → 196

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	281	4304
1	609	3989
2	2291	3588
done	5001	3580

prune341.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	12	23
done	12	23

end0.0ms

sample1.6s

Algorithm

intervals

Results

662.0ms	1464×	body	1280	valid
340.0ms	1208×	body	640	valid
257.0ms	4339×	body	80	valid
129.0ms	651×	body	320	valid
45.0ms	338×	body	160	valid