Details

sample180.0ms

Algorithm

intervals

Results

93.0ms	119×	body	1280	valid
32.0ms	72×	body	640	valid
11.0ms	256×	pre	80	true
10.0ms	39×	body	80	valid
7.0ms	22×	body	320	valid
1.0ms	4×	body	160	valid

simplify79.0ms

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	64	9
8	82	9
9	99	9
10	107	9
done	107	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.1b	(tan (+ y z))

rewrite23.0ms

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))
3.0ms	(tan (+ y z))

series336.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(+ x (- (tan (+ y z)) (tan a)))
133.0ms	(- (tan (+ y z)) (tan a))
64.0ms	(tan (+ y z))

simplify1.5s

Counts

81 → 81

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	128	1195
1	278	1008
2	650	882
3	2317	793
done	5001	792

prune255.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite162.0ms

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:

11.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
80.0ms	(+ 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))

series1.2s

Counts

4 → 12

Calls

4 calls:

253.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
399.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
446.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
108.0ms	(* (tan y) (tan z))

simplify888.0ms

Counts

239 → 239

Iterations

Useful iterations: done (879.0ms)

Iter	Nodes	Cost
0	303	7323
1	700	6202
2	1812	5656
done	5000	5633

prune854.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
2.5b	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite407.0ms

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:

83.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
50.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))
257.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series1.5s

Counts

4 → 12

Calls

4 calls:

451.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
444.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
106.0ms	(* (tan y) (tan z))
542.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify914.0ms

Counts

220 → 220

Iterations

Useful iterations: done (905.0ms)

Iter	Nodes	Cost
0	288	6913
1	637	5832
2	1609	5275
done	5000	5252

prune883.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(exp (tan a))
0.3b	(* (exp x) (/ (exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (exp (tan a))))
0.4b	(exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
24×	`exp-prod`
23×	`add-cube-cbrt`
22×	`times-frac`
16×	`associate-r`
11×	`add-cbrt-cube`
8×	`pow1`
7×	`add-exp-log`
6×	`associate-l` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `div-inv` `rem-exp-log`
1×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `pow-prod-up` `flip--` `pow-div`

Counts

4 → 99

Calls

4 calls:

6.0ms	(* (tan y) (tan z))
2.0ms	(exp (tan a))
71.0ms	(* (exp x) (/ (exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (exp (tan a))))
16.0ms	(exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))

series925.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (tan y) (tan z))
47.0ms	(exp (tan a))
516.0ms	(* (exp x) (/ (exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (exp (tan a))))
254.0ms	(exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))

simplify2.6s

Counts

111 → 111

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	200	1846
1	433	1756
2	1207	1580
3	4030	1578
done	5001	1578

prune546.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes281.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	36
1	27	36
done	27	36

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.1s	3862×	body	1280	valid
950.0ms	2021×	body	640	valid
357.0ms	8000×	pre	80	true
230.0ms	712×	body	320	valid
112.0ms	1118×	body	80	valid
61.0ms	287×	body	160	valid