Details

sample307.0ms

Algorithm

intervals

Results

118.0ms	111×	body	1280	valid
115.0ms	20×	body	2560	valid
36.0ms	56×	body	640	valid
10.0ms	23×	body	320	valid
5.0ms	36×	body	80	valid
2.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
2.4b	(tan (+ x eps))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

17.0ms	(- (tan (+ x eps)) (tan x))
11.0ms	(tan (+ x eps))

series579.0ms

Counts

2 → 6

Calls

2 calls:

110.0ms	(- (tan (+ x eps)) (tan x))
469.0ms	(tan (+ x eps))

simplify1.1s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
2	742
1	204
0	94

prune361.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
61×	`times-frac`
57×	`prod-diff`
21×	`fma-neg`
16×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`flip3--` `tan-quot` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`sub-neg` `diff-log` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 171

Calls

4 calls:

10.0ms	(- 1 (* (tan x) (tan eps)))
50.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
24.0ms	(* (tan x) (tan eps))
134.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

148.0ms	(- 1 (* (tan x) (tan eps)))
313.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
152.0ms	(* (tan x) (tan eps))
524.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.2s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2876
1	604
0	245

prune926.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
0.1b	(/ (* (sin x) (tan eps)) (cos x))
0.3b	(* (sin x) (tan eps))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

221×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
90×	`prod-diff`
44×	`difference-of-squares`
31×	`distribute-lft-out`
30×	`fma-neg`
22×	`distribute-lft-out--`
13×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`pow1` `flip3--` `div-inv` `flip--` `add-log-exp`
5×	`tan-quot` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `prod-exp` `associate-*r/` `cbrt-unprod`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

63.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
20.0ms	(/ (* (sin x) (tan eps)) (cos x))
18.0ms	(* (sin x) (tan eps))
208.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

355.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x))))
162.0ms	(/ (* (sin x) (tan eps)) (cos x))
108.0ms	(* (sin x) (tan eps))
574.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify2.6s

Counts

248 → 248

Iterations

Iter	Nodes
done	5000
2	3475
1	734
0	306

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
3.5b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

1393×	`times-frac`
890×	`add-sqr-sqrt`
851×	`*-un-lft-identity`
845×	`add-cube-cbrt`
585×	`prod-diff`
106×	`div-inv`
45×	`fma-neg`
30×	`add-cbrt-cube` `add-exp-log`
28×	`associate-/r/`
26×	`associate-r` `associate-l`
15×	`flip3--` `flip--`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `distribute-lft-out--`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub`

Counts

4 → 787

Calls

4 calls:

8.0ms	(/ (sin eps) (cos eps))
40.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
26.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
204.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series693.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (sin eps) (cos eps))
168.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
157.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
337.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

simplify2.3s

Counts

799 → 799

Iterations

Iter	Nodes
done	5000
1	2246
0	939

prune8.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.8b

regimes234.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.6b and baseline of 13.0b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample8.4s

Algorithm

intervals

Results

4.2s	3324×	body	1280	valid
1.8s	1870×	body	640	valid
1.5s	637×	body	2560	valid
268.0ms	731×	body	320	valid
200.0ms	1103×	body	80	valid
121.0ms	335×	body	160	valid