Details

sample183.0ms

Algorithm

intervals

Results

99.0ms	126×	body	1280	valid
27.0ms	60×	body	640	valid
15.0ms	23×	body	320	valid
12.0ms	256×	pre	80	true
3.0ms	37×	body	80	valid
2.0ms	10×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	31	9
4	37	9
5	47	9
6	54	9
7	66	9
8	89	9
9	103	9
10	109	9
done	109	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.8b	(tan (+ y z))

rewrite24.0ms

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:

9.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series323.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(+ x (- (tan (+ y z)) (tan a)))
128.0ms	(- (tan (+ y z)) (tan a))
60.0ms	(tan (+ y z))

simplify1.2s

Counts

81 → 81

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	128	1195
1	274	1008
2	644	882
3	2328	793
done	5001	792

prune262.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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))

rewrite156.0ms

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:

3.0ms	(+ (tan y) (tan z))
83.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
53.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (tan y) (tan z))
389.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
424.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
103.0ms	(* (tan y) (tan z))

simplify747.0ms

Counts

219 → 219

Iterations

Useful iterations: done (738.0ms)

Iter	Nodes	Cost
0	296	6641
1	656	5549
2	1703	5029
done	5000	5006

prune761.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`tan-quot` `pow1` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`
1×	`frac-times` `associate-+r+` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

6.0ms	(+ (tan y) (tan z))
3.0ms	(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a))))
0.0ms	(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a)))
5.0ms	(* (tan y) (tan z))

series886.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (tan y) (tan z))
318.0ms	(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a))))
361.0ms	(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a)))
104.0ms	(* (tan y) (tan z))

simplify1.0s

Counts

81 → 81

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	137	1281
1	319	1204
2	815	1082
3	2312	1080
done	5001	1079

prune384.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
60.7b	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `cbrt-div` `pow1/3`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (tan a))
1.0ms	(cbrt (tan a))
1.0ms	(cbrt (tan a))
1.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series619.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (tan a))
133.0ms	(cbrt (tan a))
142.0ms	(cbrt (tan a))
210.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: 4 (442.0ms)

Iter	Nodes	Cost
0	55	644
1	107	463
2	216	367
3	597	357
4	2164	307
done	5000	307

prune651.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes275.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	58
1	32	58
done	32	58

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.2s	3961×	body	1280	valid
912.0ms	1922×	body	640	valid
370.0ms	8000×	pre	80	true
217.0ms	682×	body	320	valid
114.0ms	1154×	body	80	valid
59.0ms	281×	body	160	valid