Details

sample216.0ms

Algorithm

intervals

Results

106.0ms	113×	body	1280	valid
45.0ms	18×	body	2560	valid
34.0ms	60×	body	640	valid
9.0ms	23×	body	320	valid
4.0ms	32×	body	80	valid
2.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

27.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series177.0ms

Counts

2 → 6

Calls

2 calls:

115.0ms	(- (tan (+ x eps)) (tan x))
63.0ms	(tan (+ x eps))

simplify2.7s

Counts

47 → 47

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	94	720
1	194	597
2	457	510
3	1461	450
done	5000	438

prune202.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize15.0ms

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))

rewrite259.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

32.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
18.0ms	(+ (tan x) (tan eps))
31.0ms	(* (tan x) (tan eps))
163.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

290.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
146.0ms	(+ (tan x) (tan eps))
136.0ms	(* (tan x) (tan eps))
521.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.6s

Counts

181 → 181

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	240	4762
1	560	3970
2	1558	3555
done	5000	3149

prune585.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
3.1b	(- (/ (/ (+ (tan x) (tan eps)) (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (cbrt (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite534.0ms

Algorithm

rewrite-expression-head

Rules

486×	`times-frac`
342×	`*-un-lft-identity`
312×	`add-sqr-sqrt`
306×	`prod-diff`
296×	`cbrt-div`
292×	`add-cube-cbrt`
200×	`associate-/r/`
194×	`cbrt-prod`
149×	`flip3--` `flip--`
102×	`fma-neg`
99×	`frac-times`
51×	`associate-r/` `associate-l/`
28×	`div-inv`
24×	`distribute-lft-out`
13×	`tan-quot`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `frac-sub` `distribute-lft-out--`

Counts

4 → 498

Calls

4 calls:

30.0ms	(* (tan x) (tan eps))
30.0ms	(* (tan x) (tan eps))
31.0ms	(* (tan x) (tan eps))
365.0ms	(- (/ (/ (+ (tan x) (tan eps)) (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (cbrt (- 1 (* (tan x) (tan eps))))) (tan x))

series923.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (tan x) (tan eps))
112.0ms	(* (tan x) (tan eps))
115.0ms	(* (tan x) (tan eps))
572.0ms	(- (/ (/ (+ (tan x) (tan eps)) (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (cbrt (- 1 (* (tan x) (tan eps))))) (tan x))

simplify2.2s

Counts

510 → 510

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	607	29975
1	1404	24668
2	3059	21363
done	5001	19776

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
3.1b	(- (/ (/ (+ (tan eps) (tan x)) (cbrt (- 1 (* (tan x) (tan eps))))) (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (tan x))

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
166×	`*-un-lft-identity`
132×	`add-sqr-sqrt`
126×	`prod-diff`
116×	`add-cube-cbrt`
56×	`cbrt-div`
49×	`cbrt-prod`
42×	`fma-neg`
40×	`associate-/r/`
29×	`flip3--` `flip--`
24×	`distribute-lft-out`
19×	`frac-times`
13×	`tan-quot`
11×	`associate-r/` `associate-l/`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `frac-sub` `distribute-lft-out--`

Counts

4 → 257

Calls

4 calls:

15.0ms	(* (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
301.0ms	(- (/ (/ (+ (tan eps) (tan x)) (cbrt (- 1 (* (tan x) (tan eps))))) (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (tan x))

series908.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (tan x) (tan eps))
126.0ms	(* (tan x) (tan eps))
115.0ms	(* (tan x) (tan eps))
521.0ms	(- (/ (/ (+ (tan eps) (tan x)) (cbrt (- 1 (* (tan x) (tan eps))))) (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify1.5s

Counts

269 → 269

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	346	11744
1	764	9856
2	1785	8931
done	5001	7312

prune907.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.1b

regimes230.0ms

Accuracy

94.5% (0.5b remaining)

Error of 14.0b against oracle of 13.6b and baseline of 22.2b

bsearch201.0ms

Steps

Iters	Range		Point
6	2.6348029274484795e-33	3.560853546224578e-32	8.102442873651765e-33
8	-3.80808233067461e-41	-9.726232553466861e-46	-7.133415199702495e-42

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	31	79
1	41	49
done	41	49

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.4s	3329×	body	1280	valid
1.6s	673×	body	2560	valid
1.1s	1885×	body	640	valid
262.0ms	711×	body	320	valid
138.0ms	1071×	body	80	valid
83.0ms	331×	body	160	valid