Details

sample520.0ms

Algorithm

intervals

Results

280.0ms	106×	body	1280	valid
99.0ms	24×	body	2560	valid
79.0ms	55×	body	640	valid
31.0ms	30×	body	320	valid
10.0ms	31×	body	80	valid
8.0ms	10×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize16.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
5.1b	(tan (+ x eps))

rewrite33.0ms

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:

27.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series237.0ms

Counts

2 → 6

Calls

2 calls:

154.0ms	(- (tan (+ x eps)) (tan x))
83.0ms	(tan (+ x eps))

simplify1.7s

Counts

49 → 49

Iterations

Iter	Nodes
4	3838
3	1279
2	439
1	205
0	96

prune457.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
1.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite233.0ms

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:

50.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
17.0ms	(+ (tan x) (tan eps))
30.0ms	(* (tan x) (tan eps))
131.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

365.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
120.0ms	(+ (tan x) (tan eps))
103.0ms	(* (tan x) (tan eps))
519.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.5s

Counts

185 → 185

Iterations

Iter	Nodes
3	5477
2	1575
1	579
0	242

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.0b

localize69.0ms

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)))
2.8b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite190.0ms

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:

8.0ms	(/ (sin eps) (cos eps))
22.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
34.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
78.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (sin eps) (cos eps))
165.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
139.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
369.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

simplify1.5s

Counts

803 → 803

Iterations

Iter	Nodes
1	2204
0	942

prune15.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
16.2b	(fma (/ (sin x) 1) (/ (/ 1 (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- (* (/ 1 (cos x)) (sin x))))
33.8b	(fma (- (/ 1 (cos x))) (sin x) (* (/ 1 (cos x)) (sin x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
44×	`times-frac`
32×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`associate-r` `associate-l`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

4 → 128

Calls

4 calls:

19.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
20.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.0ms	(fma (/ (sin x) 1) (/ (/ 1 (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- (* (/ 1 (cos x)) (sin x))))
0.0ms	(fma (- (/ 1 (cos x))) (sin x) (* (/ 1 (cos x)) (sin x)))

series725.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
131.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
370.0ms	(fma (/ (sin x) 1) (/ (/ 1 (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- (* (/ 1 (cos x)) (sin x))))
88.0ms	(fma (- (/ 1 (cos x))) (sin x) (* (/ 1 (cos x)) (sin x)))

simplify3.0s

Counts

140 → 140

Iterations

Iter	Nodes
3	7141
2	1696
1	475
0	173

prune2.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.0b

regimes365.0ms

Accuracy

0% (0.4b remaining)

Error of 12.8b against oracle of 12.3b and baseline of 12.8b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
3	41
2	41
1	36
0	25

end0.0ms

sample15.7s

Algorithm

intervals

Results

7.8s	3282×	body	1280	valid
3.1s	1829×	body	640	valid
2.4s	617×	body	2560	valid
1.2s	796×	body	320	valid
786.0ms	1111×	body	80	valid
234.0ms	365×	body	160	valid