Details

sample308.0ms

Algorithm

intervals

Results

194.0ms	109×	body	1280	valid
44.0ms	63×	body	640	valid
32.0ms	14×	body	2560	valid
11.0ms	23×	body	320	valid
5.0ms	37×	body	80	valid
3.0ms	10×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize21.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ eps x)) (tan x))
3.1b	(tan (+ eps x))

rewrite31.0ms

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:

20.0ms	(- (tan (+ eps x)) (tan x))
10.0ms	(tan (+ eps x))

series225.0ms

Counts

2 → 6

Calls

2 calls:

143.0ms	(- (tan (+ eps x)) (tan x))
82.0ms	(tan (+ eps x))

simplify939.0ms

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
2	698
1	196
0	94

prune267.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- (tan eps)) (tan x) 1)
0.1b	(/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1))
0.1b	(+ (tan eps) (tan x))
4.1b	(- (/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1)) (tan x))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
61×	`times-frac`
48×	`prod-diff`
17×	`distribute-lft-out`
16×	`fma-neg`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`tan-quot` `div-inv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-def` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `frac-sub` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 146

Calls

4 calls:

1.0ms	(fma (- (tan eps)) (tan x) 1)
40.0ms	(/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1))
14.0ms	(+ (tan eps) (tan x))
78.0ms	(- (/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1)) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

164.0ms	(fma (- (tan eps)) (tan x) 1)
359.0ms	(/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1))
149.0ms	(+ (tan eps) (tan x))
588.0ms	(- (/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1)) (tan x))

simplify1.7s

Counts

158 → 158

Iterations

Iter	Nodes
done	5001
2	1719
1	453
0	196

prune838.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
4.5b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (/ (sin x) (cos x)))

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

2619×	`times-frac`
1947×	`add-sqr-sqrt`
1935×	`*-un-lft-identity`
1378×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
184×	`div-inv`
84×	`fma-neg`
30×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
15×	`flip3--` `flip--`
9×	`prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `sin-mult`
2×	`clear-num` `associate-/r` `frac-2neg` `cos-mult` `associate-/l` `associate-/l/`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `unswap-sqr`

Counts

4 → 1271

Calls

4 calls:

10.0ms	(* (sin x) (sin eps))
15.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
15.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
399.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (/ (sin x) (cos x)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sin x) (sin eps))
177.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
118.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
311.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (/ (sin x) (cos x)))

simplify1.6s

Counts

1283 → 1283

Iterations

Iter	Nodes
done	5000
1	2909
0	1291

prune7.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.2b	(* (sin eps) (sin x))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
4.5b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (/ (* (sin eps) (sin x)) (cos x)) (cos eps)))) (/ (sin x) (cos x)))

rewrite674.0ms

Algorithm

rewrite-expression-head

Rules

3832×	`times-frac`
3239×	`add-sqr-sqrt`
2497×	`*-un-lft-identity`
1758×	`add-cube-cbrt`
1430×	`prod-diff`
734×	`difference-of-squares`
237×	`div-inv`
186×	`distribute-lft-out--`
110×	`fma-neg`
29×	`associate-/r/`
20×	`add-cbrt-cube` `add-exp-log`
15×	`flip3--` `flip--`
8×	`pow1`
6×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`sin-mult`
2×	`pow-prod-down` `*-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `diff-log` `cos-mult` `frac-sub` `associate-/l` `associate-/l/`

Counts

4 → 1631

Calls

4 calls:

11.0ms	(* (sin x) (sin eps))
11.0ms	(* (sin eps) (sin x))
14.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
401.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (/ (* (sin eps) (sin x)) (cos x)) (cos eps)))) (/ (sin x) (cos x)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin x) (sin eps))
58.0ms	(* (sin eps) (sin x))
119.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
300.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (/ (* (sin eps) (sin x)) (cos x)) (cos eps)))) (/ (sin x) (cos x)))

simplify1.8s

Counts

1643 → 1643

Iterations

Iter	Nodes
done	5001
1	3806
0	1714

prune8.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.1b

regimes223.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.7s	3268×	body	1280	valid
1.3s	652×	body	2560	valid
1.3s	1860×	body	640	valid
625.0ms	765×	body	320	valid
217.0ms	1081×	body	80	valid
124.0ms	374×	body	160	valid