Details

sample387.0ms

Algorithm

intervals

Results

208.0ms	106×	body	1280	valid
71.0ms	24×	body	2560	valid
62.0ms	55×	body	640	valid
21.0ms	30×	body	320	valid
7.0ms	31×	body	80	valid
5.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize20.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
5.1b	(tan (+ x eps))

rewrite50.0ms

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:

39.0ms	(- (tan (+ x eps)) (tan x))
11.0ms	(tan (+ x eps))

series197.0ms

Counts

2 → 6

Calls

2 calls:

141.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(tan (+ x eps))

simplify1.5s

Counts

33 → 33

Iterations

Iter	Nodes
5	3439
4	1447
3	676
2	287
1	139
0	70

prune365.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.8b

localize36.0ms

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))
0.2b	(* (tan x) (tan eps))
1.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite170.0ms

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))
28.0ms	(* (tan x) (tan eps))
81.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

300.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
122.0ms	(+ (tan x) (tan eps))
113.0ms	(* (tan x) (tan eps))
485.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
3	3786
2	1110
1	404
0	174

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.5b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 114

Calls

4 calls:

28.0ms	(* (tan x) (tan eps))
27.0ms	(* (tan x) (tan eps))
79.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
30.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.6s

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (tan x) (tan eps))
115.0ms	(* (tan x) (tan eps))
145.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.2s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify854.0ms

Counts

126 → 126

Iterations

Iter	Nodes
2	2595
1	633
0	204

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.7b

localize103.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (sin eps))
0.3b	(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
1.5b	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-cbrt-cube` `add-exp-log`
18×	`tan-quot`
14×	`add-sqr-sqrt`
13×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`frac-times` `associate-*l/`
7×	`associate-l`
6×	`associate-*r/` `add-log-exp`
5×	`pow-prod-down` `frac-sub`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`times-frac` `*-commutative`
2×	`flip3-+` `associate--l+` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `div-inv` `flip--`

Counts

4 → 100

Calls

4 calls:

27.0ms	(* (tan x) (tan eps))
13.0ms	(* (tan x) (sin eps))
47.0ms	(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
64.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series2.0s

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (tan x) (tan eps))
104.0ms	(* (tan x) (sin eps))
290.0ms	(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
1.5s	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify1.1s

Counts

112 → 112

Iterations

Iter	Nodes
2	3211
1	725
0	243

prune1.9s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 12.7b

regimes322.0ms

Accuracy

89.1% (0.8b remaining)

Error of 15.1b against oracle of 14.3b and baseline of 21.9b

bsearch211.0ms

Steps

Iters	Range		Point
2	1.879070068339194e-54	2.1729496112421346e-54	2.1362146683792668e-54
11	-2.7310998996894105e-29	-2.4800299462845904e-49	-2.5708003209900752e-39

simplify33.0ms

Iterations

Iter	Nodes
2	52
1	52
0	37

end0.0ms

sample14.2s

Algorithm

intervals

Results

7.5s	3282×	body	1280	valid
2.8s	1829×	body	640	valid
2.5s	617×	body	2560	valid
756.0ms	796×	body	320	valid
318.0ms	1111×	body	80	valid
230.0ms	365×	body	160	valid