Details

sample310.0ms

Algorithm

intervals

Results

133.0ms	116×	body	1280	valid
87.0ms	59×	body	640	valid
18.0ms	256×	pre	80	true
13.0ms	28×	body	320	valid
8.0ms	42×	body	80	valid
4.0ms	11×	body	160	valid

simplify140.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 13.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
3.4b	(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:

20.0ms	(- (tan (+ y z)) (tan a))
26.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(tan (+ y z))

series509.0ms

Counts

3 → 9

Calls

3 calls:

209.0ms	(- (tan (+ y z)) (tan a))
204.0ms	(+ x (- (tan (+ y z)) (tan a)))
96.0ms	(tan (+ y z))

simplify3.8s

Counts

81 → 81

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	128	1195
1	274	1008
2	641	882
3	2380	793
done	5001	773

prune326.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite507.0ms

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:

41.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
159.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
261.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
21.0ms	(* (tan y) (tan z))

series2.0s

Counts

4 → 12

Calls

4 calls:

456.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
700.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
665.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
173.0ms	(* (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

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
59.8b	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite8.0ms

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:

2.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
0.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series955.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(cbrt (tan a))
207.0ms	(cbrt (tan a))
164.0ms	(cbrt (tan a))
339.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify22.4s

Counts

64 → 64

Iterations

Useful iterations: 4 (952.0ms)

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

prune564.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (+ (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))
2.3b	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 208

Calls

4 calls:

102.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
156.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
16.0ms	(* (tan y) (tan z))
716.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series1.6s

Counts

4 → 12

Calls

4 calls:

480.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
458.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
118.0ms	(* (tan y) (tan z))
586.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify1.3s

Counts

220 → 220

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	288	6913
1	625	5832
2	1554	5275
done	5001	4644

prune780.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes327.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample8.8s

Algorithm

intervals

Results

5.1s	3866×	body	1280	valid
1.8s	1994×	body	640	valid
695.0ms	689×	body	320	valid
532.0ms	8000×	pre	80	true
217.0ms	1177×	body	80	valid
110.0ms	274×	body	160	valid