Details

sample288.0ms

Algorithm

intervals

Results

142.0ms	105×	body	1280	valid
61.0ms	17×	body	2560	valid
49.0ms	59×	body	640	valid
12.0ms	24×	body	320	valid
7.0ms	42×	body	80	valid
3.0ms	9×	body	160	valid

simplify3.0ms

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: 35.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite420.0ms

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:

35.0ms	(- (tan (+ x eps)) (tan x))
384.0ms	(tan (+ x eps))

series234.0ms

Counts

2 → 6

Calls

2 calls:

136.0ms	(- (tan (+ x eps)) (tan x))
98.0ms	(tan (+ x eps))

simplify993.0ms

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
2	742
1	204
0	94

prune316.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.2b

localize25.0ms

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))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite158.0ms

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:

33.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
11.0ms	(+ (tan x) (tan eps))
19.0ms	(* (tan x) (tan eps))
80.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

354.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
125.0ms	(+ (tan x) (tan eps))
110.0ms	(* (tan x) (tan eps))
465.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.9s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	2825
1	586
0	238

prune814.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.9b

localize87.0ms

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))
4.0b	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

95×	`times-frac`
71×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
43×	`fma-def`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
8×	`add-log-exp`
7×	`div-inv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`cbrt-undiv` `quot-tan` `clear-num` `frac-2neg` `div-exp` `distribute-lft-out`
2×	`sum-log` `distribute-rgt-neg-in`
1×	`neg-sub0` `+-commutative` `associate-+r-` `flip3-+` `unsub-neg` `neg-log` `frac-add` `flip-+` `distribute-neg-frac`

Counts

4 → 154

Calls

4 calls:

14.0ms	(/ (sin eps) (cos eps))
14.0ms	(/ (sin eps) (cos eps))
13.0ms	(/ (sin eps) (cos eps))
129.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (sin eps) (cos eps))
30.0ms	(/ (sin eps) (cos eps))
39.0ms	(/ (sin eps) (cos eps))
350.0ms	(+ (/ (/ (sin x) (cos x)) (fma (- (/ (sin x) (cos x))) (/ (sin eps) (cos eps)) 1)) (- (/ (sin x) (cos x))))

simplify1.4s

Counts

166 → 166

Iterations

Iter	Nodes
done	5002
2	1261
1	292
0	122

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(/ (* (cos eps) (cos x)) (sin eps))
0.3b	(/ (sin x) (/ (* (cos eps) (cos x)) (sin eps)))
4.0b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (* (cos eps) (cos x)) (sin eps))))) (/ (sin x) (cos x)))

rewrite756.0ms

Algorithm

rewrite-expression-head

Rules

3876×	`times-frac`
3257×	`add-sqr-sqrt`
2519×	`*-un-lft-identity`
1780×	`add-cube-cbrt`
1430×	`prod-diff`
734×	`difference-of-squares`
243×	`div-inv`
186×	`distribute-lft-out--`
110×	`fma-neg`
29×	`associate-/r/`
20×	`add-cbrt-cube` `add-exp-log`
15×	`flip3--` `flip--`
13×	`associate-/r*`
8×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`prod-exp` `cbrt-unprod`
1×	`quot-tan` `sub-neg` `diff-log` `cos-mult` `frac-sub` `associate-/l/`

Counts

4 → 1668

Calls

4 calls:

7.0ms	(/ (sin eps) (cos eps))
10.0ms	(/ (* (cos eps) (cos x)) (sin eps))
11.0ms	(/ (sin x) (/ (* (cos eps) (cos x)) (sin eps)))
496.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (* (cos eps) (cos x)) (sin eps))))) (/ (sin x) (cos x)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin eps) (cos eps))
96.0ms	(/ (* (cos eps) (cos x)) (sin eps))
131.0ms	(/ (sin x) (/ (* (cos eps) (cos x)) (sin eps)))
355.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (* (cos eps) (cos x)) (sin eps))))) (/ (sin x) (cos x)))

simplify3.5s

Counts

1680 → 1680

Iterations

Iter	Nodes
done	5001
1	3961
0	1780

prune14.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

regimes460.0ms

Accuracy

0% (0.4b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	22

end0.0ms

sample7.5s

Algorithm

intervals

Results

3.9s	3251×	body	1280	valid
1.5s	1865×	body	640	valid
1.3s	650×	body	2560	valid
359.0ms	772×	body	320	valid
124.0ms	1137×	body	80	valid
106.0ms	325×	body	160	valid