Details

sample496.0ms

Algorithm

intervals

Results

258.0ms	85×	body	1280	valid
96.0ms	63×	body	640	valid
78.0ms	20×	body	2560	valid
28.0ms	29×	body	320	valid
13.0ms	46×	body	80	valid
9.0ms	13×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize19.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (tan (+ x eps)) (tan x))
4.3b	(tan (+ x eps))

rewrite18.0ms

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:

13.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series208.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(- (tan (+ x eps)) (tan x))
84.0ms	(tan (+ x eps))

simplify3.6s

Counts

33 → 33

Iterations

Iter	Nodes
5	3750
4	1478
3	672
2	285
1	137
0	70

prune341.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize37.0ms

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))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite134.0ms

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:

36.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
66.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

325.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
154.0ms	(+ (tan x) (tan eps))
157.0ms	(* (tan x) (tan eps))
504.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
3	3734
2	1101
1	402
0	174

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.4b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`tan-quot`
19×	`*-un-lft-identity`
18×	`associate-r`
15×	`add-exp-log`
14×	`add-cube-cbrt`
11×	`times-frac` `add-cbrt-cube`
8×	`pow1` `frac-sub` `add-log-exp`
7×	`frac-times` `associate-l` `associate-*l/`
5×	`flip3-+` `frac-add` `prod-exp` `flip-+`
4×	`insert-posit16` `unswap-sqr`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `div-exp` `pow-prod-down` `associate-/r/` `un-div-inv` `*-commutative` `flip--` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `sub-neg` `diff-log` `1-exp` `div-inv`

Counts

4 → 103

Calls

4 calls:

39.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
13.0ms	(+ (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
48.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

373.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
131.0ms	(+ (tan x) (tan eps))
111.0ms	(* (tan x) (tan eps))
495.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify24.6s

Counts

115 → 115

Iterations

Iter	Nodes
3	6382
2	1783
1	566
0	227

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (+ (tan x) (tan eps)) (cos x))
9.0b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite106.0ms

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:

23.0ms	(* (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
29.0ms	(* (+ (tan x) (tan eps)) (cos x))
38.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (tan x) (tan eps))
117.0ms	(* (tan x) (tan eps))
134.0ms	(* (+ (tan x) (tan eps)) (cos x))
250.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify4.4s

Counts

98 → 98

Iterations

Iter	Nodes
3	9258
2	1915
1	543
0	174

prune976.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes120.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	24
1	24
0	20

end0.0ms

sample10.2s

Algorithm

intervals

Results

5.3s	3322×	body	1280	valid
2.1s	633×	body	2560	valid
1.6s	1785×	body	640	valid
500.0ms	823×	body	320	valid
240.0ms	1114×	body	80	valid
137.0ms	323×	body	160	valid