Details

sample546.0ms

Algorithm

intervals

Results

272.0ms	127×	body	1280	valid
145.0ms	53×	body	640	valid
85.0ms	22×	body	2560	valid
18.0ms	21×	body	320	valid
7.0ms	25×	body	80	valid
5.0ms	8×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
3.3b	(tan (+ x eps))

rewrite20.0ms

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:

14.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series201.0ms

Counts

2 → 6

Calls

2 calls:

109.0ms	(- (tan (+ x eps)) (tan x))
92.0ms	(tan (+ x eps))

simplify3.0s

Counts

49 → 49

Iterations

Iter	Nodes
4	3889
3	1289
2	437
1	203
0	96

prune533.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite154.0ms

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:

16.0ms	(+ (tan x) (tan eps))
26.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(* (tan x) (tan eps))
93.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series996.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (tan x) (tan eps))
232.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
124.0ms	(* (tan x) (tan eps))
523.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.8s

Counts

185 → 185

Iterations

Iter	Nodes
3	5205
2	1570
1	577
0	242

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.6b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
3.6b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

1393×	`times-frac`
890×	`add-sqr-sqrt`
851×	`*-un-lft-identity`
845×	`add-cube-cbrt`
585×	`prod-diff`
106×	`div-inv`
45×	`fma-neg`
30×	`add-cbrt-cube` `add-exp-log`
28×	`associate-/r/`
26×	`associate-r` `associate-l`
15×	`flip3--` `flip--`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `distribute-lft-out--`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub`

Counts

4 → 791

Calls

4 calls:

20.0ms	(/ (sin eps) (cos eps))
25.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
27.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
99.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin eps) (cos eps))
165.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
139.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
337.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

simplify1.6s

Counts

803 → 803

Iterations

Iter	Nodes
1	2202
0	942

prune15.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.6b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.3b	(* (/ (sin x) (cos x)) (sin eps))
3.6b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

1381×	`times-frac`
877×	`add-sqr-sqrt`
845×	`*-un-lft-identity`
839×	`add-cube-cbrt`
585×	`prod-diff`
105×	`div-inv`
45×	`fma-neg`
28×	`associate-/r/`
26×	`associate-l`
23×	`add-cbrt-cube` `add-exp-log`
16×	`associate-r`
15×	`flip3--` `flip--`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--`
1×	`frac-times` `quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/` `frac-sub`

Counts

4 → 773

Calls

4 calls:

19.0ms	(/ (sin eps) (cos eps))
34.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
16.0ms	(* (/ (sin x) (cos x)) (sin eps))
118.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin eps) (cos eps))
138.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
121.0ms	(* (/ (sin x) (cos x)) (sin eps))
361.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

simplify1.6s

Counts

785 → 785

Iterations

Iter	Nodes
1	2317
0	976

prune16.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.6b

regimes211.0ms

Accuracy

0% (0.3b remaining)

Error of 12.8b against oracle of 12.4b and baseline of 12.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	21
1	21
0	18

end0.0ms

sample11.3s

Algorithm

intervals

Results

6.0s	3306×	body	1280	valid
2.0s	1850×	body	640	valid
1.7s	613×	body	2560	valid
1.0s	754×	body	320	valid
289.0ms	1124×	body	80	valid
137.0ms	353×	body	160	valid