Details

sample343.0ms

Algorithm

intervals

Results

131.0ms	101×	body	1280	valid
87.0ms	61×	body	640	valid
81.0ms	29×	body	2560	valid
12.0ms	24×	body	320	valid
5.0ms	33×	body	80	valid
3.0ms	8×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize13.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (tan (+ x eps)) (tan x))
2.3b	(tan (+ x eps))

rewrite32.0ms

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:

25.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series201.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(- (tan (+ x eps)) (tan x))
101.0ms	(tan (+ x eps))

simplify964.0ms

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
2	742
1	204
0	94

prune296.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
0.1b	(+ (tan eps) (tan x))
0.2b	(* (tan eps) (tan x))
2.2b	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite168.0ms

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` `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 → 169

Calls

4 calls:

44.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
8.0ms	(+ (tan eps) (tan x))
12.0ms	(* (tan eps) (tan x))
93.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

386.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
152.0ms	(+ (tan eps) (tan x))
154.0ms	(* (tan eps) (tan x))
554.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify1.9s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	3001
1	586
0	237

prune979.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.4b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

1349×	`times-frac`
840×	`add-sqr-sqrt`
825×	`*-un-lft-identity`
819×	`add-cube-cbrt`
559×	`prod-diff`
102×	`div-inv`
43×	`fma-neg`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`cbrt-undiv` `quot-tan` `clear-num` `frac-2neg` `div-exp`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 715

Calls

4 calls:

12.0ms	(/ (sin x) (cos x))
9.0ms	(/ (sin x) (cos x))
7.0ms	(/ (sin x) (cos x))
116.0ms	(- (/ (/ (sin x) (cos x)) (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1)) (/ (sin x) (cos x)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (sin x) (cos x))
40.0ms	(/ (sin x) (cos x))
25.0ms	(/ (sin x) (cos x))
412.0ms	(- (/ (/ (sin x) (cos x)) (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1)) (/ (sin x) (cos x)))

simplify897.0ms

Counts

727 → 727

Iterations

Iter	Nodes
done	5000
1	1834
0	812

prune5.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.3b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos x))
0.3b	(cbrt (cos x))
0.3b	(cbrt (cos x))
3.5b	(- (/ (/ (sin x) (cos x)) (fma (* (/ (/ 1 (cbrt (cos x))) (cbrt (cos x))) (/ (sin x) (cbrt (cos x)))) (- (/ (sin eps) (cos eps))) 1)) (/ (sin x) (cos x)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

1322×	`times-frac`
819×	`add-sqr-sqrt`
804×	`*-un-lft-identity`
798×	`add-cube-cbrt`
559×	`prod-diff`
99×	`div-inv`
43×	`fma-neg`
9×	`cbrt-prod`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`pow1/3`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 664

Calls

4 calls:

1.0ms	(cbrt (cos x))
1.0ms	(cbrt (cos x))
1.0ms	(cbrt (cos x))
126.0ms	(- (/ (/ (sin x) (cos x)) (fma (* (/ (/ 1 (cbrt (cos x))) (cbrt (cos x))) (/ (sin x) (cbrt (cos x)))) (- (/ (sin eps) (cos eps))) 1)) (/ (sin x) (cos x)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (cos x))
130.0ms	(cbrt (cos x))
110.0ms	(cbrt (cos x))
269.0ms	(- (/ (/ (sin x) (cos x)) (fma (* (/ (/ 1 (cbrt (cos x))) (cbrt (cos x))) (/ (sin x) (cbrt (cos x)))) (- (/ (sin eps) (cos eps))) 1)) (/ (sin x) (cos x)))

simplify976.0ms

Counts

676 → 676

Iterations

Iter	Nodes
done	5000
1	1818
0	808

prune4.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.3b

regimes308.0ms

Accuracy

0% (0.5b remaining)

Error of 12.9b against oracle of 12.4b and baseline of 12.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	28

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.4s	3232×	body	1280	valid
1.4s	633×	body	2560	valid
1.4s	1874×	body	640	valid
930.0ms	759×	body	320	valid
388.0ms	367×	body	160	valid
124.0ms	1135×	body	80	valid