Details

sample274.0ms

Algorithm

intervals

Results

114.0ms	99×	body	1280	valid
66.0ms	17×	body	2560	valid
47.0ms	65×	body	640	valid
16.0ms	29×	body	320	valid
5.0ms	33×	body	80	valid
5.0ms	13×	body	160	valid

simplify5.0ms

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: 37.6b

localize14.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
4.0b	(tan (+ x eps))

rewrite35.0ms

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:

21.0ms	(- (tan (+ x eps)) (tan x))
13.0ms	(tan (+ x eps))

series257.0ms

Counts

2 → 6

Calls

2 calls:

148.0ms	(- (tan (+ x eps)) (tan x))
109.0ms	(tan (+ x eps))

simplify2.6s

Counts

47 → 47

Iterations

Useful iterations: done (2.6s)

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

prune212.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite262.0ms

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:

17.0ms	(+ (tan x) (tan eps))
62.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
31.0ms	(* (tan x) (tan eps))
145.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

137.0ms	(+ (tan x) (tan eps))
306.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
125.0ms	(* (tan x) (tan eps))
516.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.7s

Counts

181 → 181

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	240	4762
1	560	3970
2	1556	3555
done	5000	3149

prune614.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin eps) (cos eps))
0.2b	(* (tan x) (tan eps))
6.6b	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite489.0ms

Algorithm

rewrite-expression-head

Rules

153×	`*-un-lft-identity`
103×	`times-frac`
86×	`add-sqr-sqrt`
79×	`add-cube-cbrt`
63×	`prod-diff`
24×	`distribute-lft-out`
21×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
6×	`pow1` `associate-/r` `div-inv` `associate-/l` `add-log-exp`
5×	`tan-quot` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`cbrt-undiv` `quot-tan` `frac-2neg` `div-exp` `clear-num` `difference-of-squares`
1×	`frac-times` `sub-neg` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 185

Calls

4 calls:

15.0ms	(/ (sin x) (cos x))
9.0ms	(/ (sin eps) (cos eps))
15.0ms	(* (tan x) (tan eps))
429.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

series802.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (sin x) (cos x))
39.0ms	(/ (sin eps) (cos eps))
145.0ms	(* (tan x) (tan eps))
577.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.7s

Counts

197 → 197

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	313	5561
1	656	4674
2	1588	4169
done	5000	3547

prune987.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin eps) (cos eps))
0.2b	(* (tan x) (tan eps))
6.6b	(fma (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`cbrt-undiv` `quot-tan` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

9.0ms	(/ (sin x) (cos x))
9.0ms	(/ (sin eps) (cos eps))
18.0ms	(* (tan x) (tan eps))
1.0ms	(fma (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series764.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (sin x) (cos x))
42.0ms	(/ (sin eps) (cos eps))
186.0ms	(* (tan x) (tan eps))
508.0ms	(fma (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify2.1s

Counts

105 → 105

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	190	1243
1	371	1215
2	911	1084
3	2112	1082
done	5000	1080

prune645.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.2b

regimes230.0ms

Accuracy

93.5% (0.6b remaining)

Error of 13.5b against oracle of 12.9b and baseline of 22.2b

bsearch220.0ms

Steps

Iters	Range		Point
6	1.5323993806286105e-20	9.893396450191569e-20	4.975666270883717e-20
7	-0.006495210018506858	-9.497075983896804e-05	-9.642672794131258e-05

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	75
1	37	47
done	37	47

end0.0ms

sample10.5s

Algorithm

intervals

Results

4.9s	3301×	body	1280	valid
2.3s	598×	body	2560	valid
1.7s	1873×	body	640	valid
865.0ms	797×	body	320	valid
157.0ms	1085×	body	80	valid
105.0ms	346×	body	160	valid