Details

sample397.0ms

Algorithm

intervals

Results

190.0ms	95×	body	1280	valid
93.0ms	29×	body	2560	valid
57.0ms	55×	body	640	valid
22.0ms	27×	body	320	valid
19.0ms	44×	body	80	valid
2.0ms	6×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize27.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
4.3b	(tan (+ x eps))

rewrite75.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

63.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series211.0ms

Counts

2 → 6

Calls

2 calls:

127.0ms	(- (tan (+ x eps)) (tan x))
84.0ms	(tan (+ x eps))

simplify3.1s

Counts

49 → 49

Iterations

Iter	Nodes
4	3889
3	1289
2	437
1	203
0	96

prune212.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

42.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(+ (tan x) (tan eps))
29.0ms	(* (tan x) (tan eps))
93.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

300.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
121.0ms	(+ (tan x) (tan eps))
144.0ms	(* (tan x) (tan eps))
530.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.6s

Counts

185 → 185

Iterations

Iter	Nodes
3	5442
2	1570
1	577
0	242

prune679.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b	(* (sin x) (sin eps))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

181×	`*-un-lft-identity`
136×	`add-sqr-sqrt`
98×	`times-frac`
90×	`prod-diff`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
30×	`fma-neg`
25×	`distribute-lft-out`
18×	`add-cbrt-cube` `add-exp-log`
17×	`distribute-lft-out--`
9×	`associate-/r/`
8×	`add-log-exp`
6×	`pow1`
5×	`flip3--` `prod-exp` `cbrt-unprod` `div-inv` `flip--`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `tan-quot`
2×	`sin-mult`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `cos-mult` `-commutative` `frac-sub` `flip-+` `associate-/l*` `unswap-sqr` `associate-/l/`

Counts

4 → 206

Calls

4 calls:

8.0ms	(+ (tan x) (tan eps))
17.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
11.0ms	(* (sin x) (sin eps))
328.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series984.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(+ (tan x) (tan eps))
183.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
86.0ms	(* (sin x) (sin eps))
549.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify931.0ms

Counts

218 → 218

Iterations

Iter	Nodes
2	2209
1	719
0	301

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.4b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cos x) (cos eps)) (sin x))
0.3b	(/ (sin eps) (/ (* (cos x) (cos eps)) (sin x)))
0.3b	(/ (sin eps) (/ (* (cos x) (cos eps)) (sin x)))
3.9b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin eps) (/ (* (cos x) (cos eps)) (sin x))))) (/ (sin x) (cos x)))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

3900×	`times-frac`
3265×	`add-sqr-sqrt`
2527×	`*-un-lft-identity`
1788×	`add-cube-cbrt`
1430×	`prod-diff`
734×	`difference-of-squares`
247×	`div-inv`
186×	`distribute-lft-out--`
110×	`fma-neg`
30×	`associate-/r/`
27×	`add-cbrt-cube` `add-exp-log`
17×	`associate-/r*`
15×	`flip3--` `flip--`
12×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `diff-log` `cos-mult` `frac-sub` `associate-/l/`

Counts

4 → 1692

Calls

4 calls:

13.0ms	(/ (* (cos x) (cos eps)) (sin x))
16.0ms	(/ (sin eps) (/ (* (cos x) (cos eps)) (sin x)))
13.0ms	(/ (sin eps) (/ (* (cos x) (cos eps)) (sin x)))
182.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin eps) (/ (* (cos x) (cos eps)) (sin x))))) (/ (sin x) (cos x)))

series737.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (* (cos x) (cos eps)) (sin x))
152.0ms	(/ (sin eps) (/ (* (cos x) (cos eps)) (sin x)))
156.0ms	(/ (sin eps) (/ (* (cos x) (cos eps)) (sin x)))
337.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin eps) (/ (* (cos x) (cos eps)) (sin x))))) (/ (sin x) (cos x)))

simplify3.8s

Counts

1704 → 1704

Iterations

Iter	Nodes
1	3844
0	1741

prune16.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.4b

regimes297.0ms

Accuracy

0% (0.3b remaining)

Error of 12.7b against oracle of 12.4b and baseline of 12.7b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	27
1	27
0	22

end0.0ms

sample10.5s

Algorithm

intervals

Results

4.8s	3248×	body	1280	valid
2.7s	1886×	body	640	valid
1.7s	640×	body	2560	valid
733.0ms	759×	body	320	valid
213.0ms	1093×	body	80	valid
172.0ms	374×	body	160	valid