Details

sample330.0ms

Algorithm

intervals

Results

157.0ms	106×	body	1280	valid
72.0ms	57×	body	640	valid
58.0ms	19×	body	2560	valid
16.0ms	30×	body	320	valid
7.0ms	36×	body	80	valid
3.0ms	8×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize15.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (tan (+ x eps)) (tan x))
3.0b	(tan (+ x eps))

rewrite79.0ms

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:

69.0ms	(- (tan (+ x eps)) (tan x))
8.0ms	(tan (+ x eps))

series223.0ms

Counts

2 → 6

Calls

2 calls:

149.0ms	(- (tan (+ x eps)) (tan x))
73.0ms	(tan (+ x eps))

simplify2.6s

Counts

49 → 49

Iterations

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

prune252.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.2b

localize25.0ms

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))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite205.0ms

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))
39.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
25.0ms	(* (tan x) (tan eps))
119.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ (tan x) (tan eps))
314.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
164.0ms	(* (tan x) (tan eps))
581.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.5s

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
2	1636
1	580
0	242

prune827.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(* (/ (sin eps) (cos x)) (sin x))
0.2b	(* (/ (sin eps) (cos x)) (sin x))
3.0b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

rewrite641.0ms

Algorithm

rewrite-expression-head

Rules

2646×	`times-frac`
1977×	`add-sqr-sqrt`
1957×	`*-un-lft-identity`
1400×	`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-l`
16×	`add-cbrt-cube` `add-exp-log`
15×	`flip3--` `flip--`
8×	`pow1`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub`

Counts

4 → 1302

Calls

4 calls:

16.0ms	(/ (sin x) (cos x))
44.0ms	(* (/ (sin eps) (cos x)) (sin x))
31.0ms	(* (/ (sin eps) (cos x)) (sin x))
393.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin x) (cos x))
126.0ms	(* (/ (sin eps) (cos x)) (sin x))
101.0ms	(* (/ (sin eps) (cos x)) (sin x))
348.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))

simplify3.4s

Counts

1314 → 1314

Iterations

Iter	Nodes
done	5001
1	2891
0	1307

prune11.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(* (sin eps) (/ (sin x) (cos x)))
0.2b	(* (/ (sin eps) (cos x)) (sin x))
3.0b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos x))) (cos eps)))) (/ (sin x) (cos x)))

rewrite474.0ms

Algorithm

rewrite-expression-head

Rules

2646×	`times-frac`
1977×	`add-sqr-sqrt`
1957×	`*-un-lft-identity`
1400×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
185×	`div-inv`
84×	`fma-neg`
28×	`associate-/r/`
16×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
15×	`flip3--` `flip--`
8×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
2×	`pow-prod-down` `*-commutative`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-l/` `associate-r/` `frac-sub`

Counts

4 → 1302

Calls

4 calls:

10.0ms	(/ (sin x) (cos x))
21.0ms	(* (sin eps) (/ (sin x) (cos x)))
22.0ms	(* (/ (sin eps) (cos x)) (sin x))
303.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos x))) (cos eps)))) (/ (sin x) (cos x)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin x) (cos x))
105.0ms	(* (sin eps) (/ (sin x) (cos x)))
96.0ms	(* (/ (sin eps) (cos x)) (sin x))
336.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos x))) (cos eps)))) (/ (sin x) (cos x)))

simplify3.0s

Counts

1314 → 1314

Iterations

Iter	Nodes
done	5001
1	2987
0	1338

prune7.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.1b

regimes150.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	20

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.9s	3282×	body	1280	valid
1.4s	1804×	body	640	valid
1.4s	658×	body	2560	valid
298.0ms	767×	body	320	valid
118.0ms	1136×	body	80	valid
96.0ms	353×	body	160	valid