Details

sample413.0ms

Algorithm

intervals

Results

193.0ms	98×	body	1280	valid
94.0ms	54×	body	640	valid
71.0ms	22×	body	2560	valid
30.0ms	36×	body	320	valid
10.0ms	41×	body	80	valid
2.0ms	5×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (tan (+ x eps)) (tan x))
2.5b	(tan (+ x eps))

rewrite19.0ms

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:

14.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series221.0ms

Counts

2 → 6

Calls

2 calls:

148.0ms	(- (tan (+ x eps)) (tan x))
73.0ms	(tan (+ x eps))

simplify1.0s

Counts

49 → 49

Iterations

Iter	Nodes
done	2000
3	1357
2	454
1	205
0	96

prune227.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize26.0ms

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))
1.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite217.0ms

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:

48.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(+ (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
122.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

324.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
115.0ms	(+ (tan x) (tan eps))
117.0ms	(* (tan x) (tan eps))
516.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.0s

Counts

185 → 185

Iterations

Iter	Nodes
done	2000
2	1631
1	580
0	242

prune667.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(* (sin x) (/ (sin eps) (cos eps)))
0.2b	(* (sin x) (/ (sin eps) (cos eps)))
2.7b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

2646×	`times-frac`
1977×	`add-sqr-sqrt`
1957×	`*-un-lft-identity`
1400×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
185×	`div-inv`
84×	`fma-neg`
28×	`associate-/r/`
26×	`associate-r`
16×	`add-cbrt-cube` `add-exp-log`
15×	`flip3--` `flip--`
8×	`pow1`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
2×	`pow-prod-down` `associate-r/` `-commutative`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub`

Counts

4 → 1302

Calls

4 calls:

10.0ms	(/ (sin x) (cos x))
20.0ms	(* (sin x) (/ (sin eps) (cos eps)))
29.0ms	(* (sin x) (/ (sin eps) (cos eps)))
160.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (sin x) (cos x))
124.0ms	(* (sin x) (/ (sin eps) (cos eps)))
136.0ms	(* (sin x) (/ (sin eps) (cos eps)))
318.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify2.4s

Counts

1314 → 1314

Iterations

Iter	Nodes
done	2000
0	1315

prune11.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (sin eps) (cos eps)))
0.3b	(* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps))))
2.7b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
25.8b	(cbrt (* (* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps)))) (* (sin x) (/ (sin eps) (cos eps)))))

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

2627×	`times-frac`
1956×	`add-sqr-sqrt`
1941×	`*-un-lft-identity`
1384×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
183×	`div-inv`
84×	`fma-neg`
45×	`pow1` `add-cbrt-cube` `add-exp-log`
28×	`associate-/r/`
23×	`prod-exp` `cbrt-unprod`
21×	`associate-*r/`
18×	`pow-prod-down`
15×	`flip3--` `flip--`
14×	`associate-r`
7×	`cbrt-undiv` `cbrt-div` `div-exp`
6×	`frac-times` `associate-*l/` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u`
2×	`pow-plus` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow2` `sub-neg` `pow1/3` `diff-log` `swap-sqr` `pow3` `frac-sub` `rem-cbrt-cube`

Counts

4 → 1306

Calls

4 calls:

14.0ms	(* (sin x) (/ (sin eps) (cos eps)))
61.0ms	(* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps))))
130.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
168.0ms	(cbrt (* (* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps)))) (* (sin x) (/ (sin eps) (cos eps)))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sin x) (/ (sin eps) (cos eps)))
101.0ms	(* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps))))
317.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
129.0ms	(cbrt (* (* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps)))) (* (sin x) (/ (sin eps) (cos eps)))))

simplify1.9s

Counts

1318 → 1318

Iterations

Iter	Nodes
done	2000
0	1367

prune10.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.8b

regimes172.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	22

end0.0ms

sample9.4s

Algorithm

intervals

Results

5.3s	3264×	body	1280	valid
1.6s	665×	body	2560	valid
1.5s	1778×	body	640	valid
439.0ms	775×	body	320	valid
183.0ms	1149×	body	80	valid
139.0ms	369×	body	160	valid