Details

sample437.0ms

Algorithm

intervals

Results

271.0ms	120×	body	1280	valid
65.0ms	20×	body	2560	valid
65.0ms	59×	body	640	valid
9.0ms	13×	body	320	valid
7.0ms	30×	body	80	valid
7.0ms	14×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
3.0b	(tan (+ x eps))

rewrite21.0ms

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:

16.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series174.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(- (tan (+ x eps)) (tan x))
66.0ms	(tan (+ x eps))

simplify1.2s

Counts

49 → 49

Iterations

Iter	Nodes
done	2002
4	2002
3	1357
2	454
1	205
0	96

prune486.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.4b

localize45.0ms

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))
0.3b	(* (tan x) (tan eps))
3.1b	(- (/ (+ (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` `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))))
7.0ms	(+ (tan x) (tan eps))
26.0ms	(* (tan x) (tan eps))
99.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

305.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
116.0ms	(+ (tan x) (tan eps))
123.0ms	(* (tan x) (tan eps))
521.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

185 → 185

Iterations

Iter	Nodes
done	2007
3	2007
2	1631
1	580
0	242

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.5b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
0.2b	(* (sin x) (/ (sin eps) (cos eps)))
0.2b	(* (sin x) (/ (sin eps) (cos eps)))
4.2b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite265.0ms

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`
28×	`associate-/r/`
26×	`associate-r`
23×	`add-cbrt-cube` `add-exp-log`
15×	`flip3--` `flip--`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`associate-/r` `associate-r/`
2×	`pow-prod-down` `*-commutative`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub` `associate-/l*` `associate-/l/`

Counts

4 → 1298

Calls

4 calls:

15.0ms	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
16.0ms	(* (sin x) (/ (sin eps) (cos eps)))
20.0ms	(* (sin x) (/ (sin eps) (cos eps)))
145.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
108.0ms	(* (sin x) (/ (sin eps) (cos eps)))
100.0ms	(* (sin x) (/ (sin eps) (cos eps)))
327.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify2.7s

Counts

1310 → 1310

Iterations

Iter	Nodes
done	2000
1	2000
0	1323

prune21.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.4b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin x))
0.3b	(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
4.2b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (cbrt (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps))))) (cos x)))) (/ (sin x) (cos x)))
27.0b	(cbrt (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

3871×	`times-frac`
3277×	`add-sqr-sqrt`
2525×	`*-un-lft-identity`
1786×	`add-cube-cbrt`
1430×	`prod-diff`
734×	`difference-of-squares`
240×	`div-inv`
186×	`distribute-lft-out--`
110×	`fma-neg`
28×	`associate-/r/`
20×	`associate-*l/`
18×	`frac-times` `pow1` `add-cbrt-cube` `add-exp-log`
16×	`swap-sqr` `associate-r` `associate-l`
15×	`cbrt-div` `flip3--` `flip--`
14×	`associate-*r/`
9×	`sin-mult`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`pow-prod-down`
2×	`pow2` `pow-plus` `pow3` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `frac-sub` `rem-cbrt-cube` `sqr-sin`

Counts

4 → 1693

Calls

4 calls:

10.0ms	(* (sin x) (sin x))
18.0ms	(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
121.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (cbrt (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps))))) (cos x)))) (/ (sin x) (cos x)))
134.0ms	(cbrt (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (sin x) (sin x))
48.0ms	(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
233.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (cbrt (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps))))) (cos x)))) (/ (sin x) (cos x)))
87.0ms	(cbrt (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))

simplify3.1s

Counts

1705 → 1705

Iterations

Iter	Nodes
done	2001
1	2001
0	1834

prune28.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.4b

regimes198.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample9.5s

Algorithm

intervals

Results

4.9s	3313×	body	1280	valid
1.8s	1822×	body	640	valid
1.5s	656×	body	2560	valid
487.0ms	769×	body	320	valid
454.0ms	1071×	body	80	valid
139.0ms	369×	body	160	valid