Details

sample520.0ms

Algorithm

intervals

Results

309.0ms	105×	body	1280	valid
73.0ms	75×	body	640	valid
67.0ms	16×	body	2560	valid
16.0ms	15×	body	320	valid
11.0ms	32×	body	80	valid
9.0ms	13×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize22.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (tan (+ x eps)) (tan x))
4.6b	(tan (+ x eps))

rewrite941.0ms

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:

917.0ms	(- (tan (+ x eps)) (tan x))
13.0ms	(tan (+ x eps))

series949.0ms

Counts

2 → 6

Calls

2 calls:

805.0ms	(- (tan (+ x eps)) (tan x))
143.0ms	(tan (+ x eps))

simplify11.0s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
4	4053
3	1371
2	457
1	201
0	94

prune577.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
2.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite363.0ms

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:

67.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
19.0ms	(+ (tan x) (tan eps))
33.0ms	(* (tan x) (tan eps))
212.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.8s

Counts

4 → 12

Calls

4 calls:

671.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
183.0ms	(+ (tan x) (tan eps))
178.0ms	(* (tan x) (tan eps))
742.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify3.6s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
2	1645
1	586
0	240

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.1b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sin eps) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos eps))
0.2b	(* (/ (sin x) (cos x)) (sin eps))
0.2b	(* (/ (sin x) (cos x)) (sin eps))
2.7b	(- (/ (sin x) (cos x)) (/ (/ (sin x) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos x)))

rewrite747.0ms

Algorithm

rewrite-expression-head

Rules

2510×	`times-frac`
1759×	`add-sqr-sqrt`
1736×	`*-un-lft-identity`
1341×	`add-cube-cbrt`
988×	`prod-diff`
264×	`difference-of-squares`
138×	`div-inv`
133×	`distribute-lft-out--`
86×	`associate-/r/`
44×	`flip3--` `flip--`
26×	`associate-l`
24×	`associate-/l*`
19×	`add-exp-log` `add-cbrt-cube`
13×	`fma-neg`
8×	`pow1`
6×	`associate-r` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`associate-/r*`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`sub-neg` `distribute-rgt-out--` `frac-2neg` `diff-log` `clear-num` `frac-sub` `associate-/l/` `sub-div`

Counts

4 → 1212

Calls

4 calls:

92.0ms	(/ (/ (sin eps) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos eps))
39.0ms	(* (/ (sin x) (cos x)) (sin eps))
31.0ms	(* (/ (sin x) (cos x)) (sin eps))
295.0ms	(- (/ (sin x) (cos x)) (/ (/ (sin x) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos x)))

series1.9s

Counts

4 → 12

Calls

4 calls:

278.0ms	(/ (/ (sin eps) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos eps))
132.0ms	(* (/ (sin x) (cos x)) (sin eps))
130.0ms	(* (/ (sin x) (cos x)) (sin eps))
1.3s	(- (/ (sin x) (cos x)) (/ (/ (sin x) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos x)))

simplify9.0s

Counts

1224 → 1224

Iterations

Iter	Nodes
done	5000
1	3967
0	1665

prune22.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.0b

localize199.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sin eps) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos eps))
0.2b	(* (/ (sin x) (cos x)) (sin eps))
0.2b	(* (/ (sin x) (cos x)) (sin eps))
2.7b	(- (sin x) (/ (sin x) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

219×	`times-frac`
218×	`add-sqr-sqrt`
205×	`*-un-lft-identity`
140×	`add-cube-cbrt`
72×	`prod-diff`
44×	`difference-of-squares`
26×	`associate-l`
24×	`associate-/l*`
22×	`distribute-lft-out--`
19×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
10×	`div-inv`
8×	`pow1` `flip3--` `flip--`
6×	`associate-r` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg` `associate-/r*`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 276

Calls

4 calls:

93.0ms	(/ (/ (sin eps) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos eps))
39.0ms	(* (/ (sin x) (cos x)) (sin eps))
43.0ms	(* (/ (sin x) (cos x)) (sin eps))
127.0ms	(- (sin x) (/ (sin x) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

315.0ms	(/ (/ (sin eps) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))) (cos eps))
144.0ms	(* (/ (sin x) (cos x)) (sin eps))
126.0ms	(* (/ (sin x) (cos x)) (sin eps))
454.0ms	(- (sin x) (/ (sin x) (- 1 (/ (* (/ (sin x) (cos x)) (sin eps)) (cos eps)))))

simplify6.5s

Counts

288 → 288

Iterations

Iter	Nodes
done	5001
2	3949
1	1348
0	538

prune3.9s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.0b

regimes625.0ms

Accuracy

0% (0.4b remaining)

Error of 13.1b against oracle of 12.7b and baseline of 13.1b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample14.0s

Algorithm

intervals

Results

7.0s	3298×	body	1280	valid
3.2s	1846×	body	640	valid
2.4s	646×	body	2560	valid
635.0ms	742×	body	320	valid
237.0ms	1135×	body	80	valid
149.0ms	333×	body	160	valid