Details

sample817.0ms

Algorithm

intervals

Results

631.0ms	126×	body	1280	valid
78.0ms	59×	body	640	valid
31.0ms	256×	pre	80	true
24.0ms	28×	body	320	valid
10.0ms	33×	body	80	valid
6.0ms	10×	body	160	valid

simplify985.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.3b	(tan (+ y z))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`expm1-log1p-u` `pow1` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`tan-sum` `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 → 75

Calls

3 calls:

24.0ms	(+ x (- (tan (+ y z)) (tan a)))
20.0ms	(- (tan (+ y z)) (tan a))
5.0ms	(tan (+ y z))

series383.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(+ x (- (tan (+ y z)) (tan a)))
161.0ms	(- (tan (+ y z)) (tan a))
56.0ms	(tan (+ y z))

simplify870.0ms

Counts

84 → 84

Iterations

Iter	Nodes
3	2061
2	649
1	284
0	131

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `fma-def` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `associate-r` `associate-l`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 211

Calls

4 calls:

7.0ms	(+ (tan y) (tan z))
116.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
21.0ms	(* (tan y) (tan z))
76.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))

series1.2s

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ (tan y) (tan z))
493.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
103.0ms	(* (tan y) (tan z))
493.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))

simplify2.6s

Counts

223 → 223

Iterations

Iter	Nodes
3	5155
2	1709
1	686
0	301

prune3.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite513.0ms

Algorithm

rewrite-expression-head

Rules

321×	`*-un-lft-identity`
237×	`add-sqr-sqrt`
180×	`prod-diff`
172×	`times-frac`
146×	`add-cube-cbrt`
92×	`associate-+r+`
58×	`difference-of-squares`
44×	`distribute-lft-out`
30×	`fma-neg` `distribute-lft-out--`
14×	`associate-/r/`
11×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
8×	`flip3--` `div-inv` `flip--`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `tan-quot`
2×	`cbrt-undiv` `sum-log` `sub-neg` `diff-log` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod`
1×	`+-commutative` `clear-num` `associate-+r-` `frac-2neg` `flip3-+` `pow-prod-down` `-commutative` `frac-sub` `flip-+` `associate-/l` `unswap-sqr` `associate-/l/`

Counts

4 → 299

Calls

4 calls:

285.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a)))
161.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
24.0ms	(* (sin y) (tan z))
29.0ms	(/ (* (sin y) (tan z)) (cos y))

series1.4s

Counts

4 → 12

Calls

4 calls:

527.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a)))
565.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
121.0ms	(* (sin y) (tan z))
162.0ms	(/ (* (sin y) (tan z)) (cos y))

simplify942.0ms

Counts

311 → 311

Iterations

Iter	Nodes
2	2025
1	823
0	367

prune6.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(- (/ (log (exp (+ (tan z) (tan y)))) (- 1 (* (tan y) (tan z)))) (tan a))
0.5b	(exp (+ (tan z) (tan y)))
3.5b	(log (exp (+ (tan z) (tan y))))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

129×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
97×	`times-frac`
90×	`prod-diff`
65×	`log-pow`
56×	`exp-prod`
30×	`fma-neg`
19×	`pow1`
14×	`distribute-lft-out`
9×	`add-log-exp`
8×	`associate-/r/`
6×	`add-cbrt-cube` `add-exp-log`
5×	`flip3--` `tan-quot` `flip--`
4×	`expm1-log1p-u` `log-prod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`associate-r` `associate-l`
2×	`exp-sum` `difference-of-squares` `rem-exp-log`
1×	`frac-times` `sum-log` `sub-neg` `diff-log` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 200

Calls

4 calls:

18.0ms	(* (tan y) (tan z))
184.0ms	(- (/ (log (exp (+ (tan z) (tan y)))) (- 1 (* (tan y) (tan z)))) (tan a))
17.0ms	(exp (+ (tan z) (tan y)))
30.0ms	(log (exp (+ (tan z) (tan y))))

series950.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (tan y) (tan z))
529.0ms	(- (/ (log (exp (+ (tan z) (tan y)))) (- 1 (* (tan y) (tan z)))) (tan a))
133.0ms	(exp (+ (tan z) (tan y)))
140.0ms	(log (exp (+ (tan z) (tan y))))

simplify1.9s

Counts

212 → 212

Iterations

Iter	Nodes
3	4034
2	1466
1	613
0	291

prune3.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes640.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample15.1s

Algorithm

intervals

Results

8.6s	3923×	body	1280	valid
4.0s	1956×	body	640	valid
891.0ms	8000×	pre	80	true
660.0ms	708×	body	320	valid
361.0ms	1145×	body	80	valid
141.0ms	268×	body	160	valid