Details

sample529.0ms

Algorithm

intervals

Results

328.0ms	142×	body	1280	valid
109.0ms	61×	body	640	valid
33.0ms	256×	pre	80	true
17.0ms	17×	body	320	valid
8.0ms	29×	body	80	valid
5.0ms	7×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
34	2015
33	1949
32	1871
31	1805
30	1727
29	1661
28	1583
27	1517
26	1439
25	1373
24	1295
23	1229
22	1151
21	1085
20	1007
19	941
18	863
17	797
16	719
15	653
14	575
13	510
12	430
11	354
10	254
9	186
8	103
7	71
6	61
5	46
4	35
3	29
2	22
1	15
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.4b	(tan (+ y z))

rewrite59.0ms

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` `insert-posit16`
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 → 45

Calls

3 calls:

21.0ms	(+ x (- (tan (+ y z)) (tan a)))
26.0ms	(- (tan (+ y z)) (tan a))
10.0ms	(tan (+ y z))

series422.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(+ x (- (tan (+ y z)) (tan a)))
154.0ms	(- (tan (+ y z)) (tan a))
78.0ms	(tan (+ y z))

simplify2.4s

Counts

54 → 54

Iterations

Iter	Nodes
4	6132
3	1497
2	470
1	198
0	94

prune673.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

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

rewrite210.0ms

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`
4×	`insert-posit16`
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 → 71

Calls

4 calls:

12.0ms	(+ (tan y) (tan z))
107.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
71.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
17.0ms	(* (tan y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

137.0ms	(+ (tan y) (tan z))
447.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
536.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
156.0ms	(* (tan y) (tan z))

simplify1.4s

Counts

83 → 83

Iterations

Iter	Nodes
3	3320
2	1020
1	377
0	159

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (cos y) (sin z))
0.2b	(* (tan y) (tan z))
0.3b	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

133.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
10.0ms	(* (cos y) (sin z))
30.0ms	(* (tan y) (tan z))
51.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

series972.0ms

Counts

4 → 12

Calls

4 calls:

563.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
64.0ms	(* (cos y) (sin z))
115.0ms	(* (tan y) (tan z))
231.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

simplify5.6s

Counts

95 → 95

Iterations

Iter	Nodes
3	8326
2	1644
1	492
0	204

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize114.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
6.9b	(cbrt (* (tan y) (tan z)))
6.9b	(cbrt (* (tan y) (tan z)))
6.9b	(cbrt (* (tan y) (tan z)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

44×	`tan-quot`
33×	`cbrt-div`
20×	`frac-times`
14×	`associate-l/` `associate-r/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

69.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
12.0ms	(cbrt (* (tan y) (tan z)))
8.0ms	(cbrt (* (tan y) (tan z)))
16.0ms	(cbrt (* (tan y) (tan z)))

series867.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
179.0ms	(cbrt (* (tan y) (tan z)))
224.0ms	(cbrt (* (tan y) (tan z)))
195.0ms	(cbrt (* (tan y) (tan z)))

simplify2.9s

Counts

98 → 98

Iterations

Iter	Nodes
4	6304
3	1760
2	657
1	266
0	120

prune2.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes623.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	32
1	32
0	25

end0.0ms

sample14.2s

Algorithm

intervals

Results

8.8s	3931×	body	1280	valid
2.9s	2003×	body	640	valid
923.0ms	8000×	pre	80	true
742.0ms	693×	body	320	valid
284.0ms	1101×	body	80	valid
225.0ms	272×	body	160	valid