Details

sample491.0ms

Algorithm

intervals

Results

223.0ms	102×	body	1280	valid
115.0ms	51×	body	640	valid
79.0ms	19×	body	2560	valid
28.0ms	27×	body	320	valid
24.0ms	48×	body	80	valid
6.0ms	9×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize19.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
2.9b	(tan (+ x eps))

rewrite53.0ms

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:

47.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series162.0ms

Counts

2 → 6

Calls

2 calls:

104.0ms	(- (tan (+ x eps)) (tan x))
58.0ms	(tan (+ x eps))

simplify1.2s

Counts

49 → 49

Iterations

Iter	Nodes
done	2002
4	2002
3	1357
2	454
1	205
0	96

prune251.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.6b

localize42.0ms

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))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite178.0ms

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:

27.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
126.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

293.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
170.0ms	(+ (tan x) (tan eps))
137.0ms	(* (tan x) (tan eps))
504.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts

185 → 185

Iterations

Iter	Nodes
done	2007
3	2007
2	1631
1	580
0	242

prune866.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.9b

localize55.0ms

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)))
2.6b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite276.0ms

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:

12.0ms	(/ (sin x) (cos x))
16.0ms	(* (sin x) (/ (sin eps) (cos eps)))
19.0ms	(* (sin x) (/ (sin eps) (cos eps)))
174.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin x) (cos x))
89.0ms	(* (sin x) (/ (sin eps) (cos eps)))
116.0ms	(* (sin x) (/ (sin eps) (cos eps)))
375.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify2.7s

Counts

1314 → 1314

Iterations

Iter	Nodes
done	2000
1	2000
0	1315

prune12.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.8b

localize66.0ms

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)))
2.6b	(fma (/ (sin x) (cos x)) (/ 1 (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (- (/ (sin x) (cos x))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
29×	`times-frac`
28×	`*-un-lft-identity` `add-cube-cbrt`
26×	`associate-r`
16×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `associate-/r` `div-exp` `div-inv` `associate-/l`
2×	`pow-prod-down` `associate-r/` `-commutative`
1×	`quot-tan` `clear-num` `frac-2neg` `fma-udef`

Counts

4 → 112

Calls

4 calls:

16.0ms	(/ (sin x) (cos x))
30.0ms	(* (sin x) (/ (sin eps) (cos eps)))
24.0ms	(* (sin x) (/ (sin eps) (cos eps)))
0.0ms	(fma (/ (sin x) (cos x)) (/ 1 (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (- (/ (sin x) (cos x))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (sin x) (cos x))
100.0ms	(* (sin x) (/ (sin eps) (cos eps)))
118.0ms	(* (sin x) (/ (sin eps) (cos eps)))
305.0ms	(fma (/ (sin x) (cos x)) (/ 1 (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (- (/ (sin x) (cos x))))

simplify944.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	2001
3	2001
2	1235
1	395
0	171

prune787.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.8b

regimes219.0ms

Accuracy

0% (0.4b remaining)

Error of 13.2b against oracle of 12.8b and baseline of 13.2b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end0.0ms

sample10.2s

Algorithm

intervals

Results

5.5s	3297×	body	1280	valid
1.9s	641×	body	2560	valid
1.8s	1868×	body	640	valid
513.0ms	744×	body	320	valid
179.0ms	1111×	body	80	valid
117.0ms	339×	body	160	valid