Details

sample402.0ms

Algorithm

intervals

Results

167.0ms	94×	body	1280	valid
115.0ms	25×	body	2560	valid
73.0ms	66×	body	640	valid
20.0ms	25×	body	320	valid
9.0ms	37×	body	80	valid
4.0ms	9×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize69.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
2.0b	(tan (+ x eps))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

18.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series213.0ms

Counts

2 → 6

Calls

2 calls:

149.0ms	(- (tan (+ x eps)) (tan x))
64.0ms	(tan (+ x eps))

simplify1.8s

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
4	1840
3	735
2	313
1	150
0	77

prune174.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan eps) (tan x))
0.1b	(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
0.2b	(* (tan eps) (tan x))
3.0b	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite567.0ms

Algorithm

rewrite-expression-head

Rules

85×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
37×	`times-frac`
29×	`tan-quot`
26×	`difference-of-squares`
23×	`add-cube-cbrt`
19×	`frac-sub`
18×	`associate-/r*`
13×	`distribute-lft-out--` `unswap-sqr`
12×	`distribute-lft-out`
9×	`associate-l`
8×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
6×	`pow1` `associate-/l/`
4×	`insert-posit16`
3×	`flip3-+` `associate-r` `frac-add` `flip-+`
2×	`clear-num` `frac-2neg` `flip3--` `associate-/r/` `flip--`
1×	`frac-times` `cbrt-undiv` `+-commutative` `sum-log` `sub-neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 138

Calls

4 calls:

10.0ms	(+ (tan eps) (tan x))
113.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
32.0ms	(* (tan eps) (tan x))
407.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

132.0ms	(+ (tan eps) (tan x))
302.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
118.0ms	(* (tan eps) (tan x))
531.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify1.7s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	1607
1	612
0	264

prune822.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan eps) (tan x)) (- 1 (/ (* (sin eps) (tan x)) (cos eps))))
0.2b	(/ (* (sin eps) (tan x)) (cos eps))
0.2b	(* (sin eps) (tan x))
3.0b	(- (/ (+ (tan eps) (tan x)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))

rewrite919.0ms

Algorithm

rewrite-expression-head

Rules

154×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
101×	`times-frac`
49×	`add-cube-cbrt`
38×	`difference-of-squares`
26×	`tan-quot`
23×	`associate-/r*`
20×	`frac-sub` `associate-/l*`
17×	`unswap-sqr`
15×	`associate-r` `associate-l`
13×	`add-cbrt-cube` `add-exp-log`
12×	`distribute-lft-out`
7×	`distribute-lft-out--` `associate-/l/`
6×	`pow1` `add-log-exp`
5×	`*-commutative`
4×	`insert-posit16`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
2×	`flip3-+` `flip3--` `frac-add` `prod-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `flip-+` `div-inv` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down`

Counts

4 → 195

Calls

4 calls:

126.0ms	(/ (+ (tan eps) (tan x)) (- 1 (/ (* (sin eps) (tan x)) (cos eps))))
41.0ms	(/ (* (sin eps) (tan x)) (cos eps))
24.0ms	(* (sin eps) (tan x))
720.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

296.0ms	(/ (+ (tan eps) (tan x)) (- 1 (/ (* (sin eps) (tan x)) (cos eps))))
140.0ms	(/ (* (sin eps) (tan x)) (cos eps))
102.0ms	(* (sin eps) (tan x))
564.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))

simplify2.4s

Counts

207 → 207

Iterations

Iter	Nodes
done	5001
2	2557
1	909
0	382

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.8b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.9s

Algorithm

rewrite-expression-head

Rules

540×	`add-sqr-sqrt`
309×	`unswap-sqr`
238×	`tan-quot`
164×	`frac-sub`
143×	`frac-times`
132×	`associate-/r*`
129×	`*-un-lft-identity`
117×	`difference-of-squares`
84×	`pow1`
77×	`associate-*l/`
65×	`associate-l`
58×	`flip3-+` `flip-+`
52×	`swap-sqr`
51×	`associate-r`
36×	`add-cube-cbrt`
35×	`pow-prod-down`
30×	`add-cbrt-cube` `add-exp-log`
25×	`associate-*r/`
23×	`*-commutative`
17×	`prod-exp` `cbrt-unprod`
12×	`associate-/l*`
11×	`distribute-lft-out--`
9×	`associate-/l/`
8×	`associate--l+` `pow-sqr` `pow-prod-up`
6×	`add-log-exp`
4×	`distribute-rgt-in` `+-commutative` `associate-+r+` `distribute-lft-in` `pow-plus` `insert-posit16`
3×	`clear-num` `frac-2neg` `frac-add` `distribute-lft-out`
2×	`pow2`
1×	`sub-neg` `times-frac` `flip3--` `diff-log` `flip--`

Counts

4 → 390

Calls

4 calls:

28.0ms	(* (tan eps) (tan x))
109.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
119.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
47.6s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))))) (tan x))

series2.7s

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (tan eps) (tan x))
153.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
168.0ms	(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
2.2s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))))) (tan x))

simplify3.3s

Counts

402 → 402

Iterations

Iter	Nodes
done	5001
1	3486
0	1005

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.7b

regimes212.0ms

Accuracy

75.4% (1.8b remaining)

Error of 13.8b against oracle of 12.0b and baseline of 19.4b

bsearch293.0ms

Steps

Iters	Range		Point
7	8.109900204952698e-153	4.3252380094430324e-151	4.257017227961505e-151
7	-6.25213087380725e-65	-8.708505840988636e-67	-1.3766066923975014e-65

simplify9.0ms

Iterations

Iter	Nodes
done	48
1	48
0	30

end0.0ms

sample10.5s

Algorithm

intervals

Results

5.5s	3275×	body	1280	valid
2.2s	1814×	body	640	valid
1.8s	610×	body	2560	valid
467.0ms	764×	body	320	valid
226.0ms	1200×	body	80	valid
122.0ms	337×	body	160	valid