Details

sample467.0ms

Algorithm

intervals

Results

188.0ms	101×	body	1280	valid
127.0ms	55×	body	640	valid
91.0ms	28×	body	2560	valid
28.0ms	32×	body	320	valid
10.0ms	10×	body	160	valid
8.0ms	30×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize28.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
4.4b	(tan (+ x eps))

rewrite40.0ms

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:

29.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series231.0ms

Counts

2 → 6

Calls

2 calls:

141.0ms	(- (tan (+ x eps)) (tan x))
89.0ms	(tan (+ x eps))

simplify1.7s

Counts

49 → 49

Iterations

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

prune491.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize43.0ms

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))
0.3b	(* (tan x) (tan eps))
2.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite186.0ms

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:

37.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
121.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

311.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
147.0ms	(+ (tan x) (tan eps))
147.0ms	(* (tan x) (tan eps))
532.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.6s

Counts

185 → 185

Iterations

Iter	Nodes
3	5477
2	1575
1	579
0	242

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.5b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.3b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.3b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
3.1b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite172.0ms

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 x) (cos x))
19.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
19.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
77.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (sin x) (cos x))
133.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
142.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
305.0ms	(- (/ (/ (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	2190
0	932

prune15.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.3b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.3b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
3.1b	(fma (/ (sin x) (cos x)) (/ 1 (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- (/ (sin x) (cos x))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
53×	`times-frac`
40×	`*-un-lft-identity` `add-cube-cbrt`
30×	`add-cbrt-cube` `add-exp-log`
26×	`associate-r` `associate-l`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`
1×	`quot-tan` `clear-num` `frac-2neg` `fma-udef`

Counts

4 → 148

Calls

4 calls:

8.0ms	(/ (sin x) (cos x))
22.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
21.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.0ms	(fma (/ (sin x) (cos x)) (/ 1 (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- (/ (sin x) (cos x))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin x) (cos x))
117.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
129.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
293.0ms	(fma (/ (sin x) (cos x)) (/ 1 (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (- (/ (sin x) (cos x))))

simplify2.0s

Counts

160 → 160

Iterations

Iter	Nodes
3	6163
2	1685
1	499
0	185

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.4b

regimes229.0ms

Accuracy

0% (0.4b remaining)

Error of 12.9b against oracle of 12.5b and baseline of 12.9b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	26
1	26
0	20

end0.0ms

sample10.7s

Algorithm

intervals

Results

5.5s	3298×	body	1280	valid
2.0s	1761×	body	640	valid
1.8s	660×	body	2560	valid
897.0ms	806×	body	320	valid
213.0ms	1103×	body	80	valid
193.0ms	372×	body	160	valid