Details

sample283.0ms

Algorithm

intervals

Results

163.0ms	118×	body	1280	valid
45.0ms	72×	body	640	valid
13.0ms	256×	pre	80	true
8.0ms	23×	body	320	valid
4.0ms	12×	body	160	valid
4.0ms	31×	body	80	valid

simplify120.0ms

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	38	9
5	45	9
6	51	9
7	61	9
8	74	9
9	86	9
10	95	9
done	95	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.7b	(tan (+ y z))

rewrite57.0ms

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:

19.0ms	(+ x (- (tan (+ y z)) (tan a)))
26.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series524.0ms

Counts

3 → 9

Calls

3 calls:

227.0ms	(+ x (- (tan (+ y z)) (tan a)))
181.0ms	(- (tan (+ y z)) (tan a))
115.0ms	(tan (+ y z))

simplify3.5s

Counts

81 → 81

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	128	1195
1	274	1008
2	644	882
3	2382	793
done	5000	773

prune356.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
97×	`times-frac`
56×	`associate-+r+`
27×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
11×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 227

Calls

4 calls:

49.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
136.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
232.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
43.0ms	(* (tan y) (tan z))

series1.9s

Counts

4 → 12

Calls

4 calls:

347.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
652.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
687.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
163.0ms	(* (tan y) (tan z))

simplify1.6s

Counts

239 → 239

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	303	7323
1	688	6202
2	1778	5656
done	5000	5023

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (tan a))
0.7b	(cbrt (tan a))
0.7b	(cbrt (tan a))
60.6b	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite16.0ms

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:

5.0ms	(cbrt (tan a))
4.0ms	(cbrt (tan a))
4.0ms	(cbrt (tan a))
1.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series993.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt (tan a))
213.0ms	(cbrt (tan a))
217.0ms	(cbrt (tan a))
349.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify21.3s

Counts

64 → 64

Iterations

Useful iterations: 4 (814.0ms)

Iter	Nodes	Cost
0	55	644
1	107	463
2	218	367
3	572	357
4	1829	307
done	5000	307

prune410.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`tan-quot` `pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `pow-prod-down` `associate-/r/` `-commutative` `unswap-sqr`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `fma-udef` `div-inv`

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))
21.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
25.0ms	(* (tan z) (tan y))
25.0ms	(* (tan y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

323.0ms	(fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))
590.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
122.0ms	(* (tan z) (tan y))
125.0ms	(* (tan y) (tan z))

simplify1.9s

Counts

93 → 93

Iterations

Useful iterations: 3 (980.0ms)

Iter	Nodes	Cost
0	159	1853
1	353	1769
2	1093	1543
3	4040	1513
done	5000	1513

prune432.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes394.0ms

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	20	31
1	27	31
done	27	31

end0.0ms

sample8.4s

Algorithm

intervals

Results

5.1s	3881×	body	1280	valid
1.4s	2035×	body	640	valid
675.0ms	685×	body	320	valid
449.0ms	8000×	pre	80	true
230.0ms	1101×	body	80	valid
111.0ms	298×	body	160	valid