Details

sample317.0ms

Algorithm

intervals

Results

194.0ms	115×	body	1280	valid
45.0ms	50×	body	640	valid
38.0ms	14×	body	2560	valid
16.0ms	28×	body	320	valid
6.0ms	15×	body	160	valid
6.0ms	34×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize14.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.0b	(tan (+ x eps))

rewrite80.0ms

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:

74.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series556.0ms

Counts

2 → 6

Calls

2 calls:

490.0ms	(- (tan (+ x eps)) (tan x))
66.0ms	(tan (+ x eps))

simplify2.7s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	4082
3	1357
2	454
1	205
0	96

prune225.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize21.0ms

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))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite192.0ms

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:

15.0ms	(+ (tan x) (tan eps))
52.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
28.0ms	(* (tan x) (tan eps))
92.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (tan x) (tan eps))
315.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
131.0ms	(* (tan x) (tan eps))
503.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.9s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
2	1636
1	580
0	242

prune811.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (* (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))) (cos eps)))
0.2b	(* (/ (sin eps) (cos x)) (sin x))
0.2b	(* (/ (sin eps) (cos x)) (sin x))
3.2b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

2640×	`times-frac`
1971×	`add-sqr-sqrt`
1951×	`*-un-lft-identity`
1394×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
185×	`div-inv`
84×	`fma-neg`
30×	`associate-/r/`
26×	`associate-l`
19×	`add-cbrt-cube` `add-exp-log`
16×	`flip3--` `flip--`
8×	`pow1`
6×	`associate-r` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-*l/` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`associate-/l*`
2×	`pow-prod-down` `*-commutative`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `frac-sub`

Counts

4 → 1297

Calls

4 calls:

34.0ms	(/ (sin eps) (* (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))) (cos eps)))
16.0ms	(* (/ (sin eps) (cos x)) (sin x))
17.0ms	(* (/ (sin eps) (cos x)) (sin x))
123.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

series717.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (sin eps) (* (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps))) (cos eps)))
109.0ms	(* (/ (sin eps) (cos x)) (sin x))
94.0ms	(* (/ (sin eps) (cos x)) (sin x))
343.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

simplify3.2s

Counts

1309 → 1309

Iterations

Iter	Nodes
done	5001
1	2968
0	1337

prune12.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.1b

localize139.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (sin eps) (cos x)))
0.2b	(* (/ (* (sin x) (/ (sin eps) (cos x))) (cos eps)) (/ (* (sin x) (/ (sin eps) (cos x))) (cos eps)))
0.2b	(* (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)) (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))
3.2b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

rewrite401.0ms

Algorithm

rewrite-expression-head

Rules

2651×	`times-frac`
1976×	`add-sqr-sqrt`
1957×	`*-un-lft-identity`
1400×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
191×	`div-inv`
186×	`distribute-lft-out--`
169×	`add-cbrt-cube` `add-exp-log`
84×	`fma-neg`
66×	`prod-exp` `cbrt-unprod`
65×	`cbrt-undiv` `div-exp`
28×	`associate-/r/`
27×	`associate-r`
20×	`pow1`
17×	`associate-l`
15×	`flip3--` `flip--`
14×	`swap-sqr`
6×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `associate-r/` `-commutative`
2×	`pow2` `frac-times` `pow-plus` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

4 → 1382

Calls

4 calls:

26.0ms	(* (sin x) (/ (sin eps) (cos x)))
65.0ms	(* (/ (* (sin x) (/ (sin eps) (cos x))) (cos eps)) (/ (* (sin x) (/ (sin eps) (cos x))) (cos eps)))
70.0ms	(* (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)) (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))
147.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

series772.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (sin x) (/ (sin eps) (cos x)))
132.0ms	(* (/ (* (sin x) (/ (sin eps) (cos x))) (cos eps)) (/ (* (sin x) (/ (sin eps) (cos x))) (cos eps)))
171.0ms	(* (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)) (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))
368.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

simplify4.2s

Counts

1394 → 1394

Iterations

Iter	Nodes
done	5000
1	3574
0	1478

prune12.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.1b

regimes326.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	42
1	42
0	32

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.8s	3317×	body	1280	valid
1.5s	618×	body	2560	valid
1.3s	1856×	body	640	valid
354.0ms	765×	body	320	valid
114.0ms	1108×	body	80	valid
80.0ms	336×	body	160	valid