Details

sample475.0ms

Algorithm

intervals

Results

293.0ms	132×	body	1280	valid
76.0ms	65×	body	640	valid
21.0ms	256×	pre	80	true
15.0ms	22×	body	320	valid
7.0ms	33×	body	80	valid
2.0ms	4×	body	160	valid

simplify10.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	33	9
4	39	9
5	89	9
6	193	9
7	451	9
8	1380	9
9	4837	9
done	5001	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.9b	(tan (+ y z))

rewrite97.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

34.0ms	(+ x (- (tan (+ y z)) (tan a)))
45.0ms	(- (tan (+ y z)) (tan a))
13.0ms	(tan (+ y z))

series622.0ms

Counts

3 → 9

Calls

3 calls:

260.0ms	(+ x (- (tan (+ y z)) (tan a)))
247.0ms	(- (tan (+ y z)) (tan a))
115.0ms	(tan (+ y z))

simplify1.3s

Counts

81 → 81

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	128	1195
1	283	1011
2	1003	882
done	5000	795

prune708.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite614.0ms

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` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `sum-log`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

318.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
19.0ms	(+ (tan y) (tan z))
210.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
43.0ms	(* (tan y) (tan z))

series2.2s

Counts

4 → 12

Calls

4 calls:

814.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
221.0ms	(+ (tan y) (tan z))
931.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
222.0ms	(* (tan y) (tan z))

simplify3.7s

Counts

219 → 219

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	296	6641
1	701	5567
2	2715	5029
done	5001	4679

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
4.7b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`tan-quot`
35×	`*-un-lft-identity`
25×	`add-cube-cbrt`
20×	`pow1` `times-frac`
12×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l/` `difference-of-squares`
10×	`frac-sub`
9×	`frac-times` `associate-r/` `associate-r` `associate-l` `associate-l/`
6×	`swap-sqr`
5×	`associate-/r*` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 141

Calls

4 calls:

39.0ms	(* (tan y) (tan z))
30.0ms	(* (tan z) (tan z))
25.0ms	(* (tan y) (tan y))
111.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

series882.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(* (tan y) (tan z))
79.0ms	(* (tan z) (tan z))
71.0ms	(* (tan y) (tan y))
516.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

simplify3.7s

Counts

153 → 153

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	227	2229
1	621	2027
2	3808	1891
done	5002	1889

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
0.6b	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
2.9b	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

rewrite578.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
89×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
54×	`prod-diff`
53×	`times-frac`
18×	`cbrt-prod` `fma-neg`
12×	`unpow-prod-down` `cube-prod` `distribute-lft-out`
10×	`difference-of-squares`
8×	`associate-/r/`
7×	`tan-quot` `pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
6×	`cube-div` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `cbrt-div` `associate-r` `associate-l` `frac-sub`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`frac-times` `pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 179

Calls

4 calls:

193.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
33.0ms	(* (tan y) (tan z))
176.0ms	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
157.0ms	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

series3.2s

Counts

4 → 12

Calls

4 calls:

920.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
209.0ms	(* (tan y) (tan z))
1.3s	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
783.0ms	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

simplify3.6s

Counts

191 → 191

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	270	6095
1	726	5139
2	3508	4535
done	5002	4532

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes850.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	30
1	22	30
done	22	30

end0.0ms

sample12.8s

Algorithm

intervals

Results

7.3s	3929×	body	1280	valid
2.6s	1975×	body	640	valid
893.0ms	8000×	pre	80	true
590.0ms	272×	body	160	valid
431.0ms	664×	body	320	valid
204.0ms	1160×	body	80	valid