Details

sample315.0ms

Algorithm

intervals

Results

167.0ms	104×	body	1280	valid
50.0ms	21×	body	2560	valid
45.0ms	52×	body	640	valid
12.0ms	28×	body	320	valid
5.0ms	16×	body	160	valid
5.0ms	35×	body	80	valid

simplify18.0ms

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: 34.1b

localize72.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite86.0ms

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:

61.0ms	(- (tan (+ x eps)) (tan x))
22.0ms	(tan (+ x eps))

series404.0ms

Counts

2 → 6

Calls

2 calls:

265.0ms	(- (tan (+ x eps)) (tan x))
138.0ms	(tan (+ x eps))

simplify7.5s

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
4	4037
3	1342
2	455
1	205
0	96

prune727.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.1b

localize96.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite393.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
57×	`prod-diff`
49×	`times-frac`
21×	`fma-neg`
13×	`distribute-lft-out`
10×	`add-log-exp`
8×	`associate-/r/`
7×	`tan-quot`
6×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `difference-of-squares`
1×	`frac-times` `+-commutative` `sum-log` `flip3-+` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

18.0ms	(- 1 (* (tan x) (tan eps)))
20.0ms	(+ (tan x) (tan eps))
41.0ms	(* (tan x) (tan eps))
295.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.9s

Counts

4 → 12

Calls

4 calls:

285.0ms	(- 1 (* (tan x) (tan eps)))
228.0ms	(+ (tan x) (tan eps))
222.0ms	(* (tan x) (tan eps))
1.1s	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify8.8s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
3	4926
2	1507
1	570
0	243

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.0b

localize171.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.9b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-cbrt-cube` `add-exp-log`
19×	`frac-times` `pow-prod-down`
13×	`associate-l/` `associate-r/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 111

Calls

4 calls:

55.0ms	(* (tan x) (tan eps))
37.0ms	(* (tan x) (tan eps))
214.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series2.9s

Counts

4 → 12

Calls

4 calls:

253.0ms	(* (tan x) (tan eps))
215.0ms	(* (tan x) (tan eps))
334.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.1s	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify3.6s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	1588
1	448
0	160

prune1.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.0b

localize190.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (tan x) (tan x)) (* (tan eps) (tan eps)))
0.2b	(* (tan eps) (tan eps))
0.3b	(* (tan x) (tan x))
2.9b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
40×	`tan-quot`
20×	`add-cbrt-cube` `add-exp-log`
19×	`frac-times`
16×	`add-sqr-sqrt` `pow-prod-down`
13×	`associate-l/` `associate-r/`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
6×	`pow-plus` `swap-sqr` `pow-prod-up`
4×	`pow2` `expm1-log1p-u` `pow-sqr` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 120

Calls

4 calls:

247.0ms	(* (* (tan x) (tan x)) (* (tan eps) (tan eps)))
44.0ms	(* (tan eps) (tan eps))
47.0ms	(* (tan x) (tan x))
3.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series2.7s

Counts

4 → 12

Calls

4 calls:

360.0ms	(* (* (tan x) (tan x)) (* (tan eps) (tan eps)))
108.0ms	(* (tan eps) (tan eps))
99.0ms	(* (tan x) (tan x))
2.1s	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify4.5s

Counts

132 → 132

Iterations

Iter	Nodes
done	5003
2	1952
1	554
0	184

prune1.6s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 13.9b

regimes921.0ms

Accuracy

83.6% (1.2b remaining)

Error of 15.1b against oracle of 14.0b and baseline of 21.0b

bsearch297.0ms

Steps

Iters	Range		Point
8	1.980106668111445e-74	1.4011542472758516e-71	8.448789684450496e-72
8	-5.1266664932071965e-87	-1.4042772886075332e-89	-5.060005299698439e-87

simplify16.0ms

Iterations

Iter	Nodes
done	40
1	40
0	28

end0.0ms

sample9.5s

Algorithm

intervals

Results

4.6s	3245×	body	1280	valid
2.0s	1924×	body	640	valid
1.5s	617×	body	2560	valid
740.0ms	760×	body	320	valid
250.0ms	1085×	body	80	valid
146.0ms	369×	body	160	valid