Details

sample277.0ms

Algorithm

intervals

Results

159.0ms	111×	body	1280	valid
52.0ms	20×	body	2560	valid
35.0ms	56×	body	640	valid
10.0ms	23×	body	320	valid
5.0ms	36×	body	80	valid
3.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize26.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ eps x)) (tan x))
2.4b	(tan (+ eps x))

rewrite67.0ms

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:

56.0ms	(- (tan (+ eps x)) (tan x))
11.0ms	(tan (+ eps x))

series277.0ms

Counts

2 → 6

Calls

2 calls:

197.0ms	(- (tan (+ eps x)) (tan x))
80.0ms	(tan (+ eps x))

simplify758.0ms

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
2	698
1	196
0	94

prune286.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan eps) (tan x))
0.1b	(fma (- (tan eps)) (tan x) 1)
0.1b	(/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1))
2.1b	(- (/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1)) (tan x))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
61×	`times-frac`
48×	`prod-diff`
17×	`distribute-lft-out`
16×	`fma-neg`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`tan-quot` `div-inv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-def` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `frac-sub` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 146

Calls

4 calls:

14.0ms	(+ (tan eps) (tan x))
1.0ms	(fma (- (tan eps)) (tan x) 1)
42.0ms	(/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1))
98.0ms	(- (/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1)) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

125.0ms	(+ (tan eps) (tan x))
190.0ms	(fma (- (tan eps)) (tan x) 1)
338.0ms	(/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1))
612.0ms	(- (/ (+ (tan eps) (tan x)) (fma (- (tan eps)) (tan x) 1)) (tan x))

simplify1.7s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	1729
1	453
0	196

prune851.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

localize112.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
3.5b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

1393×	`times-frac`
890×	`add-sqr-sqrt`
851×	`*-un-lft-identity`
845×	`add-cube-cbrt`
585×	`prod-diff`
106×	`div-inv`
45×	`fma-neg`
30×	`add-cbrt-cube` `add-exp-log`
28×	`associate-/r/`
26×	`associate-r` `associate-l`
15×	`flip3--` `flip--`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `distribute-lft-out--`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub`

Counts

4 → 787

Calls

4 calls:

8.0ms	(/ (sin eps) (cos eps))
23.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
23.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
142.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series645.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin eps) (cos eps))
125.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
132.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
367.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

simplify1.2s

Counts

799 → 799

Iterations

Iter	Nodes
done	5000
1	2246
0	939

prune5.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.8b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.3b	(* (sin x) (/ (sin eps) (cos eps)))
3.5b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

1381×	`times-frac`
877×	`add-sqr-sqrt`
845×	`*-un-lft-identity`
839×	`add-cube-cbrt`
585×	`prod-diff`
105×	`div-inv`
45×	`fma-neg`
28×	`associate-/r/`
26×	`associate-r`
23×	`add-cbrt-cube` `add-exp-log`
16×	`associate-l`
15×	`flip3--` `flip--`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `associate-r/` `-commutative` `distribute-lft-out--`
1×	`frac-times` `quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*l/` `frac-sub`

Counts

4 → 769

Calls

4 calls:

12.0ms	(/ (sin eps) (cos eps))
27.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
26.0ms	(* (sin x) (/ (sin eps) (cos eps)))
137.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (sin eps) (cos eps))
138.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
130.0ms	(* (sin x) (/ (sin eps) (cos eps)))
327.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

simplify1.1s

Counts

781 → 781

Iterations

Iter	Nodes
done	5000
1	2350
0	973

prune5.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.8b

regimes260.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.6b and baseline of 13.0b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	41
2	41
1	38
0	28

end0.0ms

sample8.9s

Algorithm

intervals

Results

4.3s	3324×	body	1280	valid
1.9s	637×	body	2560	valid
1.5s	1870×	body	640	valid
439.0ms	335×	body	160	valid
367.0ms	731×	body	320	valid
152.0ms	1103×	body	80	valid