Details

sample432.0ms

Algorithm

intervals

Results

304.0ms	48×	body	1280	valid
26.0ms	40×	body	640	valid
18.0ms	133×	body	80	valid
10.0ms	22×	body	320	valid
4.0ms	13×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

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))) (fma (tan x) (tan x) 1.0))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite48.0ms

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)
15.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
6.0ms	(- 1.0 (* (tan x) (tan x)))
19.0ms	(* (tan x) (tan x))

series762.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(fma (tan x) (tan x) 1.0)
374.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
144.0ms	(- 1.0 (* (tan x) (tan x)))
139.0ms	(* (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	891	1345
3	2810	1320
done	5000	1314

prune497.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (fma (tan x) (tan x) 1.0))
0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(* (sin x) (tan x))
0.2b	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-cube-cbrt`
27×	`times-frac`
21×	`prod-diff`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `div-exp` `associate-r` `associate-l` `associate-/l/`
2×	`tan-quot` `flip3--` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `flip--` `cbrt-unprod`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

69.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (fma (tan x) (tan x) 1.0))
32.0ms	(/ (* (sin x) (tan x)) (cos x))
27.0ms	(* (sin x) (tan x))
24.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (fma (tan x) (tan x) 1.0))
81.0ms	(/ (* (sin x) (tan x)) (cos x))
70.0ms	(* (sin x) (tan x))
97.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))

simplify1.8s

Counts

137 → 137

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	232	3121
1	531	2750
2	1719	2370
done	5001	2128

prune615.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (sqrt 1.0) (sqrt 1.0) (* (- (sin x)) (/ (tan x) (cos x)))) (fma (tan x) (tan x) 1.0))
0.2b	(/ (tan x) (cos x))
0.2b	(* (- (sin x)) (/ (tan x) (cos x)))
0.2b	(fma (sqrt 1.0) (sqrt 1.0) (* (- (sin x)) (/ (tan x) (cos x))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
13×	`add-exp-log` `associate-r` `add-cbrt-cube`
10×	`associate-l`
6×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `distribute-lft-neg-in` `distribute-rgt-neg-in` `div-exp` `div-inv`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `distribute-lft-neg-out` `neg-mul-1` `associate-r/` `pow-prod-down` `-commutative` `fma-udef` `associate-/l/`

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ (fma (sqrt 1.0) (sqrt 1.0) (* (- (sin x)) (/ (tan x) (cos x)))) (fma (tan x) (tan x) 1.0))
7.0ms	(/ (tan x) (cos x))
37.0ms	(* (- (sin x)) (/ (tan x) (cos x)))
1.0ms	(fma (sqrt 1.0) (sqrt 1.0) (* (- (sin x)) (/ (tan x) (cos x))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(/ (fma (sqrt 1.0) (sqrt 1.0) (* (- (sin x)) (/ (tan x) (cos x)))) (fma (tan x) (tan x) 1.0))
60.0ms	(/ (tan x) (cos x))
108.0ms	(* (- (sin x)) (/ (tan x) (cos x)))
173.0ms	(fma (sqrt 1.0) (sqrt 1.0) (* (- (sin x)) (/ (tan x) (cos x))))

simplify1.4s

Counts

123 → 123

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	201	2136
1	451	1890
2	1420	1680
done	5000	1676

prune644.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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:

7.0ms	(pow (cos x) 2)
7.0ms	(pow (cos x) 2)
8.0ms	(pow (sin x) 2)
9.0ms	(pow (sin x) 2)

series117.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (cos x) 2)
28.0ms	(pow (cos x) 2)
33.0ms	(pow (sin x) 2)
38.0ms	(pow (sin x) 2)

simplify3.4s

Counts

92 → 92

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	68	616
1	138	530
2	293	466
3	807	466
4	3813	458
done	5000	458

prune337.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes210.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	19
1	16	19
done	16	19

end0.0ms

sample2.2s

Algorithm

intervals

Results

927.0ms	1533×	body	1280	valid
504.0ms	1249×	body	640	valid
342.0ms	4322×	body	80	valid
164.0ms	599×	body	320	valid
60.0ms	297×	body	160	valid