Details

sample331.0ms

Algorithm

intervals

Results

135.0ms	99×	body	1280	valid
58.0ms	26×	body	80	valid
57.0ms	76×	body	640	valid
43.0ms	15×	body	2560	valid
14.0ms	27×	body	320	valid
4.0ms	13×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize13.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (tan (+ x eps)) (tan x))
3.8b	(tan (+ x eps))

rewrite24.0ms

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:

17.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series533.0ms

Counts

2 → 6

Calls

2 calls:

430.0ms	(- (tan (+ x eps)) (tan x))
103.0ms	(tan (+ x eps))

simplify1.1s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
2	742
1	204
0	94

prune339.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.7b

localize43.0ms

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))
2.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite191.0ms

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:

27.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms	(+ (tan x) (tan eps))
12.0ms	(* (tan x) (tan eps))
132.0ms	(- (/ (+ (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))))
132.0ms	(+ (tan x) (tan eps))
138.0ms	(* (tan x) (tan eps))
534.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.1s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	2825
1	586
0	238

prune922.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

95×	`times-frac`
71×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
43×	`fma-def`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
8×	`add-log-exp`
7×	`div-inv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`cbrt-undiv` `quot-tan` `clear-num` `frac-2neg` `div-exp` `distribute-lft-out`
2×	`sum-log` `distribute-rgt-neg-in`
1×	`neg-sub0` `+-commutative` `associate-+r-` `flip3-+` `unsub-neg` `neg-log` `frac-add` `flip-+` `distribute-neg-frac`

Counts

4 → 154

Calls

4 calls:

7.0ms	(/ (sin eps) (cos eps))
10.0ms	(/ (sin eps) (cos eps))
15.0ms	(/ (sin eps) (cos eps))
137.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin eps) (cos eps))
40.0ms	(/ (sin eps) (cos eps))
42.0ms	(/ (sin eps) (cos eps))
302.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

simplify1.5s

Counts

166 → 166

Iterations

Iter	Nodes
done	5002
2	1261
1	292
0	122

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.0b

localize97.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `quot-tan` `clear-num` `frac-2neg` `div-exp` `div-inv`
1×	`fma-udef`

Counts

4 → 100

Calls

4 calls:

7.0ms	(/ (sin eps) (cos eps))
12.0ms	(/ (sin eps) (cos eps))
14.0ms	(/ (sin eps) (cos eps))
1.0ms	(fma (/ (sin x) (cos x)) (/ 1 (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (sin eps) (cos eps))
38.0ms	(/ (sin eps) (cos eps))
38.0ms	(/ (sin eps) (cos eps))
317.0ms	(fma (/ (sin x) (cos x)) (/ 1 (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

simplify1.9s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
3	3618
2	698
1	204
0	100

prune885.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.0b

regimes324.0ms

Accuracy

0% (0.2b remaining)

Error of 12.8b against oracle of 12.6b and baseline of 12.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample10.9s

Algorithm

intervals

Results

4.6s	3318×	body	1280	valid
3.1s	1779×	body	640	valid
2.0s	656×	body	2560	valid
557.0ms	772×	body	320	valid
220.0ms	1114×	body	80	valid
117.0ms	361×	body	160	valid