Details

sample236.0ms

Algorithm

intervals

Results

134.0ms	115×	body	1280	valid
35.0ms	50×	body	640	valid
33.0ms	14×	body	2560	valid
12.0ms	28×	body	320	valid
5.0ms	15×	body	160	valid
5.0ms	34×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune67.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize35.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.0b	(tan (+ x eps))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `tan-quot` `add-log-exp`
2×	`pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 27

Calls

2 calls:

13.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series201.0ms

Counts

2 → 6

Calls

2 calls:

138.0ms	(- (tan (+ x eps)) (tan x))
64.0ms	(tan (+ x eps))

simplify1.7s

Counts

33 → 33

Iterations

Iter	Nodes
done	5001
4	1821
3	719
2	300
1	139
0	70

prune170.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`insert-posit16` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `flip3--` `frac-add` `associate-/r/` `flip-+` `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` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

14.0ms	(+ (tan x) (tan eps))
46.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
28.0ms	(* (tan x) (tan eps))
97.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (tan x) (tan eps))
330.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
107.0ms	(* (tan x) (tan eps))
539.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	4143
2	1152
1	405
0	174

prune578.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.1b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `swap-sqr` `flip--`

Counts

4 → 114

Calls

4 calls:

29.0ms	(* (tan x) (tan eps))
28.0ms	(* (tan x) (tan eps))
125.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
39.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.7s

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (tan x) (tan eps))
103.0ms	(* (tan x) (tan eps))
177.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.3s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify1.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5028
2	2740
1	664
0	205

prune734.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b	(* (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))
3.1b	(+ (* 1 (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (* (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x)))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

89×	`tan-quot`
87×	`pow1`
44×	`frac-times`
40×	`add-cbrt-cube` `add-exp-log`
38×	`associate-*r/`
37×	`pow-prod-down`
34×	`associate-*l/`
29×	`*-un-lft-identity`
28×	`associate-r`
22×	`prod-exp` `cbrt-unprod`
20×	`times-frac`
18×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
10×	`frac-add`
9×	`add-log-exp`
8×	`pow-sqr` `pow-prod-up` `difference-of-squares`
7×	`frac-sub`
6×	`distribute-lft-out`
4×	`pow-plus` `insert-posit16`
3×	`associate-l` `*-commutative`
2×	`pow2` `cbrt-undiv` `associate-+r+` `sum-log` `flip3--` `swap-sqr` `div-exp` `associate-/r/` `flip--`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+` `div-inv` `sub-div`

Counts

4 → 180

Calls

4 calls:

73.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
80.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
65.0ms	(* (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))
100.0ms	(+ (* 1 (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (* (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x)))

series1.9s

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
152.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
452.0ms	(* (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))
1.2s	(+ (* 1 (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (* (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x)))

simplify3.2s

Counts

192 → 192

Iterations

Iter	Nodes
done	5000
2	4655
1	1102
0	320

prune1.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.9b

regimes412.0ms

Accuracy

88.6% (0.8b remaining)

Error of 15.1b against oracle of 14.3b and baseline of 21.4b

bsearch353.0ms

Steps

Iters	Range		Point
9	1.2523620733929687e-77	2.4540588509345504e-72	2.4150728912939454e-72
9	-5.984165099293203e-09	-2.0017119239229129e-16	-2.0286038026990939e-16

simplify21.0ms

Iterations

Iter	Nodes
done	59
1	59
0	43

end0.0ms

sample11.4s

Algorithm

intervals

Results

5.9s	3317×	body	1280	valid
2.3s	1856×	body	640	valid
1.9s	618×	body	2560	valid
574.0ms	765×	body	320	valid
285.0ms	1108×	body	80	valid
119.0ms	336×	body	160	valid