Details

sample312.0ms

Algorithm

intervals

Results

151.0ms	116×	body	1280	valid
61.0ms	74×	body	640	valid
26.0ms	36×	body	80	valid
17.0ms	256×	pre	80	true
13.0ms	22×	body	320	valid
3.0ms	8×	body	160	valid

simplify7.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	4724
8	1354
7	446
6	193
5	89
4	39
3	33
2	22
1	15
0	9

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize38.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.5b	(tan (+ y z))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

25.0ms	(+ x (- (tan (+ y z)) (tan a)))
27.0ms	(- (tan (+ y z)) (tan a))
11.0ms	(tan (+ y z))

series553.0ms

Counts

3 → 9

Calls

3 calls:

215.0ms	(+ x (- (tan (+ y z)) (tan a)))
229.0ms	(- (tan (+ y z)) (tan a))
109.0ms	(tan (+ y z))

simplify1.3s

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
3	1734
2	475
1	198
0	91

prune423.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l` `distribute-lft-out`
2×	`+-commutative` `associate-+r+` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `times-frac` `flip3--` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

12.0ms	(+ (tan y) (tan z))
137.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
108.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
12.0ms	(* (tan y) (tan z))

series1.8s

Counts

4 → 12

Calls

4 calls:

161.0ms	(+ (tan y) (tan z))
703.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
726.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
193.0ms	(* (tan y) (tan z))

simplify1.3s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1179
1	376
0	155

prune735.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (/ (* (- (tan y) (tan z)) (+ (tan z) (tan y))) (- (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
0.4b	(* (- (tan y) (tan z)) (+ (tan z) (tan y)))
3.8b	(/ (* (- (tan y) (tan z)) (+ (tan z) (tan y))) (- (tan y) (tan z)))

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

39×	`tan-quot`
25×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`frac-times`
15×	`associate-/l/`
13×	`add-cbrt-cube` `add-exp-log`
10×	`flip3--` `frac-sub` `add-cube-cbrt` `flip--`
8×	`pow1` `flip3-+` `associate-l` `frac-add` `flip-+`
7×	`associate-r` `associate-l/` `associate-r/`
6×	`times-frac` `add-log-exp`
5×	`associate-/r*` `difference-of-squares`
4×	`distribute-lft-out--`
3×	`prod-exp` `associate-/r/` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 118

Calls

4 calls:

166.0ms	(- (/ (/ (* (- (tan y) (tan z)) (+ (tan z) (tan y))) (- (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (tan a))
12.0ms	(* (tan y) (tan z))
91.0ms	(* (- (tan y) (tan z)) (+ (tan z) (tan y)))
55.0ms	(/ (* (- (tan y) (tan z)) (+ (tan z) (tan y))) (- (tan y) (tan z)))

series1.4s

Counts

4 → 12

Calls

4 calls:

605.0ms	(- (/ (/ (* (- (tan y) (tan z)) (+ (tan z) (tan y))) (- (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (tan a))
143.0ms	(* (tan y) (tan z))
448.0ms	(* (- (tan y) (tan z)) (+ (tan z) (tan y)))
155.0ms	(/ (* (- (tan y) (tan z)) (+ (tan z) (tan y))) (- (tan y) (tan z)))

simplify1.2s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
1	770
0	247

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize139.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ (tan z) (tan y)) (+ (tan z) (tan y)))
0.4b	(* (- (tan y) (tan z)) (- (tan y) (tan z)))
3.8b	(/ (cbrt (* (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z))) (* (* (+ (tan z) (tan y)) (+ (tan z) (tan y))) (+ (tan z) (tan y))))) (- (tan y) (tan z)))
7.9b	(cbrt (* (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z))) (* (* (+ (tan z) (tan y)) (+ (tan z) (tan y))) (+ (tan z) (tan y)))))

rewrite5.2s

Algorithm

rewrite-expression-head

Rules

28692×	`frac-times`
24610×	`tan-quot`
8190×	`cbrt-div`
7044×	`associate-*l/`
6153×	`flip3--` `frac-sub` `flip--`
6152×	`flip3-+` `frac-add` `flip-+`
4095×	`associate-/l/`
3972×	`associate-*r/`
61×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
20×	`times-frac`
18×	`pow1`
13×	`swap-sqr`
11×	`distribute-lft-out--`
10×	`add-exp-log`
9×	`add-cbrt-cube` `associate-r` `associate-l` `difference-of-squares`
7×	`cbrt-prod`
6×	`distribute-lft-out`
5×	`associate-/r*`
4×	`associate-/l*` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r/`
2×	`pow2` `sub-neg` `pow-plus` `pow3` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/3` `div-exp` `rem-cbrt-cube` `div-inv`

Counts

4 → 8343

Calls

4 calls:

68.0ms	(* (+ (tan z) (tan y)) (+ (tan z) (tan y)))
100.0ms	(* (- (tan y) (tan z)) (- (tan y) (tan z)))
929.0ms	(/ (cbrt (* (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z))) (* (* (+ (tan z) (tan y)) (+ (tan z) (tan y))) (+ (tan z) (tan y))))) (- (tan y) (tan z)))
926.0ms	(cbrt (* (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z))) (* (* (+ (tan z) (tan y)) (+ (tan z) (tan y))) (+ (tan z) (tan y)))))

series793.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (+ (tan z) (tan y)) (+ (tan z) (tan y)))
156.0ms	(* (- (tan y) (tan z)) (- (tan y) (tan z)))
144.0ms	(/ (cbrt (* (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z))) (* (* (+ (tan z) (tan y)) (+ (tan z) (tan y))) (+ (tan z) (tan y))))) (- (tan y) (tan z)))
338.0ms	(cbrt (* (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z))) (* (* (+ (tan z) (tan y)) (+ (tan z) (tan y))) (+ (tan z) (tan y)))))

simplify18.4s

Counts

8355 → 8355

Iterations

Iter	Nodes
done	13328
0	13328

prune1.9m

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes392.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	22

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.2s	3836×	body	1280	valid
1.7s	2060×	body	640	valid
818.0ms	8000×	pre	80	true
281.0ms	720×	body	320	valid
208.0ms	1113×	body	80	valid
63.0ms	271×	body	160	valid