Details

sample405.0ms

Algorithm

intervals

Results

204.0ms	98×	body	1280	valid
78.0ms	22×	body	2560	valid
68.0ms	54×	body	640	valid
30.0ms	36×	body	320	valid
9.0ms	41×	body	80	valid
2.0ms	5×	body	160	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: 35.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (tan (+ x eps)) (tan x))
2.5b	(tan (+ x eps))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `tan-quot` `add-log-exp`
2×	`pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 27

Calls

2 calls:

40.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series237.0ms

Counts

2 → 6

Calls

2 calls:

150.0ms	(- (tan (+ x eps)) (tan x))
87.0ms	(tan (+ x eps))

simplify891.0ms

Counts

33 → 33

Iterations

Iter	Nodes
done	2009
4	1821
3	719
2	300
1	139
0	70

prune217.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.7b

localize44.0ms

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))
0.2b	(* (tan x) (tan eps))
1.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`insert-posit16` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `flip3--` `frac-add` `associate-/r/` `flip-+` `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` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

46.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(+ (tan x) (tan eps))
29.0ms	(* (tan x) (tan eps))
107.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

312.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
125.0ms	(+ (tan x) (tan eps))
133.0ms	(* (tan x) (tan eps))
527.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify846.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
2	1148
1	405
0	174

prune518.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
5.8b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `insert-posit16` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

22.0ms	(* (+ (tan x) (tan eps)) (cos x))
21.0ms	(* (tan x) (tan eps))
13.0ms	(* (tan x) (tan eps))
49.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series797.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (+ (tan x) (tan eps)) (cos x))
136.0ms	(* (tan x) (tan eps))
165.0ms	(* (tan x) (tan eps))
328.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify1.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	2000
2	1970
1	541
0	174

prune595.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin eps) (cos x)) (/ (* (sin x) (sin x)) (cos eps)))
0.2b	(* (tan x) (tan eps))
0.2b	(* (/ (cos x) (cos eps)) (sin eps))
0.2b	(* (sin x) (sin x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
34×	`add-cbrt-cube` `add-exp-log`
32×	`associate-l`
27×	`*-un-lft-identity` `add-cube-cbrt`
26×	`times-frac`
17×	`pow1`
16×	`associate-r`
12×	`prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `div-exp` `unswap-sqr`
4×	`pow-prod-down` `tan-quot` `*-commutative` `insert-posit16` `add-log-exp`
3×	`swap-sqr` `associate-*l/` `div-inv`
2×	`frac-times` `associate-*r/`
1×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up` `sqr-sin` `sin-mult`

Counts

4 → 132

Calls

4 calls:

39.0ms	(* (/ (sin eps) (cos x)) (/ (* (sin x) (sin x)) (cos eps)))
13.0ms	(* (tan x) (tan eps))
14.0ms	(* (/ (cos x) (cos eps)) (sin eps))
11.0ms	(* (sin x) (sin x))

series387.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (/ (sin eps) (cos x)) (/ (* (sin x) (sin x)) (cos eps)))
119.0ms	(* (tan x) (tan eps))
108.0ms	(* (/ (cos x) (cos eps)) (sin eps))
34.0ms	(* (sin x) (sin x))

simplify497.0ms

Counts

144 → 144

Iterations

Iter	Nodes
done	2002
1	704
0	255

prune953.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes291.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample14.9s

Algorithm

intervals

Results

7.4s	3264×	body	1280	valid
3.0s	1778×	body	640	valid
2.5s	665×	body	2560	valid
727.0ms	775×	body	320	valid
595.0ms	369×	body	160	valid
373.0ms	1149×	body	80	valid