Details

sample306.0ms

Algorithm

intervals

Results

144.0ms	109×	body	1280	valid
69.0ms	23×	body	2560	valid
54.0ms	58×	body	640	valid
10.0ms	19×	body	320	valid
7.0ms	35×	body	80	valid
4.0ms	12×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune86.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize22.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (tan (+ x eps)) (tan x))
3.6b	(tan (+ x eps))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

15.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series224.0ms

Counts

2 → 6

Calls

2 calls:

145.0ms	(- (tan (+ x eps)) (tan x))
79.0ms	(tan (+ x eps))

simplify846.0ms

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
2	742
1	204
0	94

prune304.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
0.1b	(+ (tan eps) (tan x))
0.2b	(* (tan eps) (tan x))
2.9b	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite162.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

40.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
11.0ms	(+ (tan eps) (tan x))
13.0ms	(* (tan eps) (tan x))
91.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

335.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
150.0ms	(+ (tan eps) (tan x))
136.0ms	(* (tan eps) (tan x))
612.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify2.0s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	3001
1	586
0	237

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.6b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(/ (sin eps) (cos eps))
0.2b	(/ (sin eps) (cos eps))
3.7b	(- (/ (/ (sin x) (cos x)) (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1)) (/ (sin x) (cos x)))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

1349×	`times-frac`
840×	`add-sqr-sqrt`
825×	`*-un-lft-identity`
819×	`add-cube-cbrt`
559×	`prod-diff`
102×	`div-inv`
43×	`fma-neg`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`cbrt-undiv` `quot-tan` `clear-num` `frac-2neg` `div-exp`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 715

Calls

4 calls:

7.0ms	(/ (sin eps) (cos eps))
7.0ms	(/ (sin eps) (cos eps))
7.0ms	(/ (sin eps) (cos eps))
137.0ms	(- (/ (/ (sin x) (cos x)) (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1)) (/ (sin x) (cos x)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (sin eps) (cos eps))
27.0ms	(/ (sin eps) (cos eps))
34.0ms	(/ (sin eps) (cos eps))
362.0ms	(- (/ (/ (sin x) (cos x)) (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1)) (/ (sin x) (cos x)))

simplify893.0ms

Counts

727 → 727

Iterations

Iter	Nodes
done	5001
1	1884
0	841

prune5.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.5b

localize134.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(/ (sin eps) (cos eps))
17.2b	(fma (/ (/ (sin x) (cbrt (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1))) (cbrt (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1))) (/ 1 (* (cbrt (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1)) (cos x))) (/ (- (sin x)) (cos x)))
31.6b	(fma (/ -1 (cos x)) (sin x) (/ (sin x) (cos x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `quot-tan` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 80

Calls

4 calls:

14.0ms	(/ (sin eps) (cos eps))
14.0ms	(/ (sin eps) (cos eps))
1.0ms	(fma (/ (/ (sin x) (cbrt (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1))) (cbrt (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1))) (/ 1 (* (cbrt (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1)) (cos x))) (/ (- (sin x)) (cos x)))
1.0ms	(fma (/ -1 (cos x)) (sin x) (/ (sin x) (cos x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin eps) (cos eps))
40.0ms	(/ (sin eps) (cos eps))
874.0ms	(fma (/ (/ (sin x) (cbrt (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1))) (cbrt (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1))) (/ 1 (* (cbrt (fma (/ (sin x) (cos x)) (- (/ (sin eps) (cos eps))) 1)) (cos x))) (/ (- (sin x)) (cos x)))
92.0ms	(fma (/ -1 (cos x)) (sin x) (/ (sin x) (cos x)))

simplify2.0s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	4247
2	770
1	234
0	120

prune958.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.5b

regimes293.0ms

Accuracy

0% (0.4b remaining)

Error of 12.7b against oracle of 12.3b and baseline of 12.7b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample11.9s

Algorithm

intervals

Results

5.9s	3210×	body	1280	valid
2.0s	622×	body	2560	valid
1.9s	1922×	body	640	valid
1.4s	825×	body	320	valid
178.0ms	1067×	body	80	valid
129.0ms	354×	body	160	valid