Details

sample308.0ms

Algorithm

intervals

Results

145.0ms	110×	body	1280	valid
70.0ms	50×	body	640	valid
49.0ms	22×	body	2560	valid
15.0ms	30×	body	320	valid
6.0ms	16×	body	160	valid
4.0ms	28×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize19.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite68.0ms

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:

33.0ms	(- (tan (+ x eps)) (tan x))
33.0ms	(tan (+ x eps))

series198.0ms

Counts

2 → 6

Calls

2 calls:

126.0ms	(- (tan (+ x eps)) (tan x))
72.0ms	(tan (+ x eps))

simplify1.1s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
2	742
1	204
0	94

prune279.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.5b

localize34.0ms

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))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite175.0ms

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:

34.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
13.0ms	(+ (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
97.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

276.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
141.0ms	(+ (tan x) (tan eps))
165.0ms	(* (tan x) (tan eps))
531.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.5s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	2825
1	586
0	238

prune928.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize106.0ms

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))))

rewrite164.0ms

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 x) (cos x))
9.0ms	(/ (sin x) (cos x))
14.0ms	(/ (sin x) (cos x))
129.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (sin x) (cos x))
37.0ms	(/ (sin x) (cos x))
41.0ms	(/ (sin x) (cos x))
379.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

simplify2.1s

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
2	1265
1	286
0	119

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize174.0ms

Local error

Found 4 expressions with local error:

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

rewrite421.0ms

Algorithm

rewrite-expression-head

Rules

213×	`times-frac`
141×	`*-un-lft-identity`
129×	`fma-def`
117×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`add-log-exp`
13×	`div-inv`
9×	`distribute-lft-out`
6×	`sum-log` `distribute-rgt-neg-in` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`neg-sub0` `+-commutative` `associate-+r-` `associate-/r` `flip3-+` `unsub-neg` `neg-log` `frac-add` `flip-+` `distribute-neg-frac` `associate-/l`
1×	`cbrt-undiv` `quot-tan` `clear-num` `frac-2neg` `div-exp`

Counts

4 → 222

Calls

4 calls:

13.0ms	(/ (sin x) (cos x))
114.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))
152.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))
123.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin x) (cos x))
323.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))
309.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))
361.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

simplify2.2s

Counts

234 → 234

Iterations

Iter	Nodes
done	5000
2	1265
1	286
0	119

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

regimes239.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	28
1	28
0	20

end0.0ms

sample10.1s

Algorithm

intervals

Results

5.9s	3309×	body	1280	valid
1.7s	655×	body	2560	valid
1.4s	1843×	body	640	valid
604.0ms	775×	body	320	valid
147.0ms	1098×	body	80	valid
100.0ms	320×	body	160	valid