Details

sample427.0ms

Algorithm

intervals

Results

200.0ms	112×	body	1280	valid
100.0ms	19×	body	2560	valid
78.0ms	60×	body	640	valid
22.0ms	24×	body	320	valid
9.0ms	33×	body	80	valid
3.0ms	8×	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: 35.4b

localize21.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
2.8b	(tan (+ x eps))

rewrite43.0ms

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:

15.0ms	(- (tan (+ x eps)) (tan x))
27.0ms	(tan (+ x eps))

series176.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(- (tan (+ x eps)) (tan x))
65.0ms	(tan (+ x eps))

simplify3.7s

Counts

33 → 33

Iterations

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

prune330.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize22.0ms

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))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`tan-quot`
6×	`pow1`
4×	`insert-posit16` `distribute-lft-out` `associate-/l*`
3×	`associate-/r` `flip3--` `associate-r` `associate-l*` `flip--` `associate-/l/`
2×	`sub-neg` `diff-log` `associate-/r/` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

9.0ms	(- 1 (* (tan x) (tan eps)))
40.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(* (tan x) (tan eps))
88.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

163.0ms	(- 1 (* (tan x) (tan eps)))
364.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
117.0ms	(* (tan x) (tan eps))
456.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts

101 → 101

Iterations

Iter	Nodes
3	3780
2	1126
1	419
0	175

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.4b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
4.5b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (/ (sin x) (cos x)))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-cbrt-cube` `add-exp-log`
29×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`times-frac`
9×	`prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-cube-cbrt` `add-log-exp` `difference-of-squares`
4×	`insert-posit16` `distribute-lft-out--`
3×	`associate-r` `associate-l` `sin-mult`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-/r/` `cos-mult` `div-inv` `associate-/l` `associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

13.0ms	(* (sin x) (sin eps))
25.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
32.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
340.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (/ (sin x) (cos x)))

series587.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin x) (sin eps))
128.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
127.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
275.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (/ (sin x) (cos x)))

simplify9.1s

Counts

103 → 103

Iterations

Iter	Nodes
3	13556
2	1642
1	414
0	162

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.4b

localize127.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
0.3b	(/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps)))) (* (cos eps) (cos x)))
4.5b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps)))) (* (cos eps) (cos x))))) (/ (sin x) (cos x)))
24.8b	(cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))))

rewrite590.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`sin-mult`
21×	`add-exp-log`
19×	`add-cbrt-cube`
18×	`times-frac`
17×	`*-un-lft-identity`
14×	`cbrt-div`
10×	`frac-times` `associate-*l/`
8×	`associate-/l/`
6×	`cbrt-undiv` `div-exp` `associate-*r/` `add-cube-cbrt` `add-log-exp` `difference-of-squares`
5×	`prod-exp` `cbrt-unprod` `associate-/l*`
4×	`pow1` `insert-posit16` `distribute-lft-out--`
3×	`cbrt-prod`
2×	`clear-num` `associate-/r*` `frac-2neg` `associate-/r/` `cos-mult` `div-inv`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `pow3` `frac-sub` `rem-cbrt-cube` `flip--`

Counts

4 → 97

Calls

4 calls:

34.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
73.0ms	(/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps)))) (* (cos eps) (cos x)))
338.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps)))) (* (cos eps) (cos x))))) (/ (sin x) (cos x)))
141.0ms	(cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
113.0ms	(/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps)))) (* (cos eps) (cos x)))
350.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps)))) (* (cos eps) (cos x))))) (/ (sin x) (cos x)))
89.0ms	(cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))))

simplify6.0s

Counts

109 → 109

Iterations

Iter	Nodes
3	11649
2	1698
1	482
0	209

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.4b

regimes252.0ms

Accuracy

0% (0.4b remaining)

Error of 12.8b against oracle of 12.4b and baseline of 12.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	24
1	24
0	21

end0.0ms

sample11.0s

Algorithm

intervals

Results

5.8s	3368×	body	1280	valid
2.2s	1859×	body	640	valid
1.9s	593×	body	2560	valid
481.0ms	759×	body	320	valid
220.0ms	1101×	body	80	valid
116.0ms	320×	body	160	valid