Details

sample239.0ms

Algorithm

intervals

Results

43.0ms	47×	body	1280	valid
26.0ms	44×	body	640	valid
20.0ms	138×	body	80	valid
8.0ms	20×	body	320	valid
2.0ms	7×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

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))) (fma (tan x) (tan x) 1.0))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))

rewrite96.0ms

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:

1.0ms	(fma (tan x) (tan x) 1.0)
28.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
12.0ms	(- 1.0 (* (tan x) (tan x)))
50.0ms	(* (tan x) (tan x))

series489.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(fma (tan x) (tan x) 1.0)
221.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
52.0ms	(- 1.0 (* (tan x) (tan x)))
73.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

109 → 109

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	155	1557
1	371	1472
2	1607	1347
done	5000	1335

prune441.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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:

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

series111.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sin x) 2)
30.0ms	(pow (sin x) 2)
20.0ms	(pow (cos x) 2)
29.0ms	(pow (cos x) 2)

simplify1.2s

Counts

92 → 92

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	68	616
1	194	530
2	664	466
3	2409	466
done	5001	466

prune364.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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:

4.0ms	(pow (sin x) 2)
5.0ms	(pow (sin x) 2)
4.0ms	(pow (cos x) 2)
4.0ms	(pow (cos x) 2)

series88.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)
18.0ms	(pow (cos x) 2)
18.0ms	(pow (cos x) 2)

simplify1.2s

Counts

92 → 92

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	68	616
1	194	530
2	664	466
3	2409	466
done	5001	466

prune462.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
48×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
11×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/` `add-log-exp`
7×	`flip3--` `flip3-+` `flip--` `flip-+`
6×	`pow1` `fma-def` `fma-neg` `associate-r`
4×	`expm1-log1p-u` `associate-r/` `associate-l` `associate-l/` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `times-frac` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `sum-log` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 164

Calls

4 calls:

20.0ms	(+ (sqrt 1.0) (tan x))
56.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (fma (tan x) (tan x) 1.0))
23.0ms	(- (sqrt 1.0) (tan x))
82.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (sqrt 1.0) (tan x))
294.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (fma (tan x) (tan x) 1.0))
76.0ms	(- (sqrt 1.0) (tan x))
156.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))

simplify595.0ms

Counts

176 → 176

Iterations

Useful iterations: done (588.0ms)

Iter	Nodes	Cost
0	237	4048
1	721	3232
done	5000	2742

prune593.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes158.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	15	25
done	15	25

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.3s	1483×	body	1280	valid
1.2s	1239×	body	640	valid
824.0ms	4344×	body	80	valid
691.0ms	618×	body	320	valid
129.0ms	316×	body	160	valid