Details

sample427.0ms

Algorithm

intervals

Results

187.0ms	95×	body	1280	valid
94.0ms	29×	body	2560	valid
68.0ms	55×	body	640	valid
49.0ms	27×	body	320	valid
11.0ms	44×	body	80	valid
3.0ms	6×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize21.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
4.3b	(tan (+ x eps))

rewrite19.0ms

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))

series219.0ms

Counts

2 → 6

Calls

2 calls:

139.0ms	(- (tan (+ x eps)) (tan x))
80.0ms	(tan (+ x eps))

simplify1.2s

Counts

33 → 33

Iterations

Iter	Nodes
done	2017
5	2017
4	1821
3	719
2	300
1	139
0	70

prune455.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize46.0ms

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))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite199.0ms

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:

48.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(+ (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
107.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

302.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
147.0ms	(+ (tan x) (tan eps))
128.0ms	(* (tan x) (tan eps))
499.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
3	2000
2	1148
1	405
0	174

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b	(* (sin x) (sin eps))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

7.0ms	(+ (tan x) (tan eps))
27.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
24.0ms	(* (sin x) (sin eps))
288.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series835.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(+ (tan x) (tan eps))
157.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
88.0ms	(* (sin x) (sin eps))
449.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify1.3s

Counts

87 → 87

Iterations

Iter	Nodes
done	2137
3	2137
2	1533
1	426
0	169

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
3.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

14.0ms	(+ (tan x) (tan eps))
29.0ms	(/ (* (tan x) (sin eps)) (cos eps))
25.0ms	(* (tan x) (sin eps))
150.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series958.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ (tan x) (tan eps))
145.0ms	(/ (* (tan x) (sin eps)) (cos eps))
99.0ms	(* (tan x) (sin eps))
564.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify1.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	2001
3	2001
2	1206
1	399
0	166

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.4b

regimes314.0ms

Accuracy

90.5% (0.7b remaining)

Error of 15.0b against oracle of 14.3b and baseline of 21.5b

bsearch473.0ms

Steps

Iters	Range		Point
8	9.842915194399427e-41	7.297743511366456e-37	7.203202361914666e-37
11	-0.030639508246526274	-2.729201958508851e-30	-2.686281805292481e-23

simplify7.0ms

Iterations

Iter	Nodes
done	41
1	41
0	29

end0.0ms

sample15.3s

Algorithm

intervals

Results

8.4s	3248×	body	1280	valid
2.7s	640×	body	2560	valid
2.6s	1886×	body	640	valid
751.0ms	759×	body	320	valid
358.0ms	1093×	body	80	valid
278.0ms	374×	body	160	valid