Details

sample296.0ms

Algorithm

intervals

Results

166.0ms	97×	body	1280	valid
55.0ms	74×	body	640	valid
34.0ms	11×	body	2560	valid
15.0ms	29×	body	320	valid
5.0ms	36×	body	80	valid
3.0ms	9×	body	160	valid

simplify20.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
4.8b	(tan (+ x eps))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

33.0ms	(- (tan (+ x eps)) (tan x))
8.0ms	(tan (+ x eps))

series289.0ms

Counts

2 → 6

Calls

2 calls:

149.0ms	(- (tan (+ x eps)) (tan x))
139.0ms	(tan (+ x eps))

simplify1.2s

Counts: 31 → 31

prune139.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`tan-quot`
6×	`pow1`
4×	`distribute-lft-out` `associate-/l*`
3×	`flip3--` `associate-r` `associate-l` `associate-/r*` `flip--` `associate-/l/`
2×	`sub-neg` `diff-log` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

7.0ms	(- 1 (* (tan x) (tan eps)))
54.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
29.0ms	(* (tan x) (tan eps))
147.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

151.0ms	(- 1 (* (tan x) (tan eps)))
323.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
143.0ms	(* (tan x) (tan eps))
591.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify722.0ms

Counts: 97 → 97

prune382.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.5b

localize38.0ms

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)))
2.1b	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
41×	`tan-quot`
21×	`add-sqr-sqrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
10×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`pow-sqr` `pow-prod-up`
3×	`times-frac` `*-commutative` `difference-of-squares`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `sub-neg` `flip3--` `diff-log` `swap-sqr` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 108

Calls

4 calls:

19.0ms	(* (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
98.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
277.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

series1.7s

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (tan x) (tan eps))
111.0ms	(* (tan x) (tan eps))
139.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.4s	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))

simplify997.0ms

Counts: 120 → 120

prune422.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.5b

localize61.0ms

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)) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
2.1b	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (+ 1 (* (tan x) (tan eps))))) (tan x))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log` `add-cbrt-cube`
25×	`prod-exp` `cbrt-unprod`
22×	`add-sqr-sqrt`
17×	`tan-quot`
13×	`pow1`
12×	`associate-r`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`cbrt-undiv` `div-exp`
7×	`frac-times` `associate-l` `associate-*l/`
6×	`add-log-exp`
5×	`associate-*r/` `pow-prod-down`
4×	`times-frac`
3×	`*-commutative` `difference-of-squares`
2×	`unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `associate-/r/` `cos-mult` `frac-sub` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 103

Calls

4 calls:

20.0ms	(* (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
88.0ms	(* (* (tan x) (tan eps)) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
184.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (+ 1 (* (tan x) (tan eps))))) (tan x))

series2.4s

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (tan x) (tan eps))
135.0ms	(* (tan x) (tan eps))
302.0ms	(* (* (tan x) (tan eps)) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
1.8s	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (+ 1 (* (tan x) (tan eps))))) (tan x))

simplify1.6s

Counts: 115 → 115

prune572.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.5b

regimes226.0ms

Accuracy

85.4% (1.0b remaining)

Error of 15.5b against oracle of 14.5b and baseline of 21.5b

bsearch294.0ms

Steps

Iters	Range		Point
8	4.608983638651436e-103	1.5313485409075155e-100	1.5128029396190957e-100
10	-5.021841202152694e-20	-1.5006166145218615e-36	-1.4465652249682627e-28

simplify591.0ms

end0.0ms

sample10.6s

Algorithm

intervals

Results

5.1s	3327×	body	1280	valid
2.0s	616×	body	2560	valid
1.9s	1821×	body	640	valid
600.0ms	1135×	body	80	valid
476.0ms	755×	body	320	valid
104.0ms	346×	body	160	valid