Details

sample371.0ms

Algorithm

intervals

Results

176.0ms	106×	body	1280	valid
97.0ms	21×	body	2560	valid
56.0ms	56×	body	640	valid
15.0ms	21×	body	320	valid
8.0ms	37×	body	80	valid
6.0ms	15×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize26.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (tan (+ x eps)) (tan x))
2.5b	(tan (+ x eps))

rewrite70.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

58.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series226.0ms

Counts

2 → 6

Calls

2 calls:

143.0ms	(- (tan (+ x eps)) (tan x))
82.0ms	(tan (+ x eps))

simplify2.7s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	4082
3	1357
2	454
1	205
0	96

prune207.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.6b

localize22.0ms

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

rewrite173.0ms

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` `insert-posit16` `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 → 173

Calls

4 calls:

44.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
100.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

296.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
120.0ms	(+ (tan x) (tan eps))
127.0ms	(* (tan x) (tan eps))
469.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.1s

Counts

185 → 185

Iterations

Iter	Nodes
done	5001
2	1631
1	580
0	242

prune830.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.5b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b	(pow (* (tan x) (tan eps)) 3)
3.0b	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1`
40×	`tan-quot`
21×	`add-cbrt-cube` `add-exp-log`
19×	`frac-times` `pow-prod-down`
13×	`associate-l/` `associate-r/`
10×	`prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `associate-l` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `pow-unpow`
2×	`pow-pow` `pow-plus` `pow-exp` `*-commutative` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `swap-sqr` `fma-udef` `unswap-sqr` `sqr-pow`

Counts

4 → 115

Calls

4 calls:

15.0ms	(* (tan x) (tan eps))
98.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
15.0ms	(pow (* (tan x) (tan eps)) 3)
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

series1.7s

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (tan x) (tan eps))
146.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
169.0ms	(pow (* (tan x) (tan eps)) 3)
1.2s	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

simplify2.9s

Counts

127 → 127

Iterations

Iter	Nodes
done	5667
2	2816
1	710
0	216

prune901.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.9b

localize259.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
0.4b	(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
0.4b	(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
3.1b	(- (+ (fma (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x)))))) (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (/ (sin x) (cos x))) (+ (/ (/ (* (sin eps) (* (* (sin eps) (sin x)) (* (sin eps) (sin x)))) (* (* (* (cos eps) (cos x)) (* (cos eps) (cos x))) (cos eps))) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x)))))) (/ (sin eps) (* (cos eps) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x))))))))) (/ (/ (sin x) (cos x)) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))

rewrite526.0ms

Algorithm

rewrite-expression-head

Rules

121×	`pow1`
79×	`*-un-lft-identity`
52×	`prod-diff`
51×	`add-sqr-sqrt` `pow-prod-down`
46×	`add-cube-cbrt`
40×	`add-cbrt-cube` `add-exp-log`
37×	`times-frac`
24×	`prod-exp` `cbrt-unprod`
15×	`distribute-lft-out`
12×	`pow-sqr` `cos-mult` `pow-prod-up`
9×	`add-log-exp`
6×	`pow-plus`
4×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`pow2` `frac-times` `swap-sqr` `associate-r` `associate-l` `associate-l/` `associate-r/` `*-commutative`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sum-log` `sub-neg` `flip3-+` `flip3--` `associate--l+` `flip-+` `flip--`

Counts

4 → 199

Calls

4 calls:

46.0ms	(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
80.0ms	(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
78.0ms	(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
314.0ms	(- (+ (fma (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x)))))) (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (/ (sin x) (cos x))) (+ (/ (/ (* (sin eps) (* (* (sin eps) (sin x)) (* (sin eps) (sin x)))) (* (* (* (cos eps) (cos x)) (* (cos eps) (cos x))) (cos eps))) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x)))))) (/ (sin eps) (* (cos eps) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x))))))))) (/ (/ (sin x) (cos x)) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))

series1.8s

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
56.0ms	(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
64.0ms	(* (* (cos eps) (cos x)) (* (cos eps) (cos x)))
1.6s	(- (+ (fma (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x)))))) (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x)) (/ (sin x) (cos x))) (+ (/ (/ (* (sin eps) (* (* (sin eps) (sin x)) (* (sin eps) (sin x)))) (* (* (* (cos eps) (cos x)) (* (cos eps) (cos x))) (cos eps))) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x)))))) (/ (sin eps) (* (cos eps) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x))))))))) (/ (/ (sin x) (cos x)) (- 1 (* (/ (* (sin eps) (sin x)) (* (* (cos eps) (cos x)) (* (cos eps) (cos x)))) (/ (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (cos eps) (cos x))))))) (/ (sin x) (cos x)))

simplify3.6s

Counts

211 → 211

Iterations

Iter	Nodes
done	5079
2	3429
1	825
0	291

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes213.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	44
1	44
0	34

end0.0ms

sample13.7s

Algorithm

intervals

Results

7.4s	3287×	body	1280	valid
2.8s	1828×	body	640	valid
2.1s	629×	body	2560	valid
633.0ms	758×	body	320	valid
339.0ms	360×	body	160	valid
247.0ms	1138×	body	80	valid