Details

sample178.0ms

Algorithm

intervals

Results

103.0ms	127×	body	1280	valid
26.0ms	61×	body	640	valid
12.0ms	256×	pre	80	true
7.0ms	23×	body	320	valid
4.0ms	17×	body	160	valid
3.0ms	28×	body	80	valid

simplify104.0ms

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	61	9
7	84	9
8	107	9
9	137	9
10	164	9
done	164	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

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))
3.9b	(tan (+ y z))

rewrite26.0ms

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))

series316.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(+ x (- (tan (+ y z)) (tan a)))
125.0ms	(- (tan (+ y z)) (tan a))
57.0ms	(tan (+ y z))

simplify1.5s

Counts

81 → 81

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	128	1195
1	283	1008
2	710	882
3	2723	793
done	5000	792

prune254.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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))))
0.1b	(+ (tan y) (tan z))
0.2b	(* (tan y) (tan z))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
56×	`associate-+r+`
54×	`prod-diff`
48×	`times-frac`
16×	`distribute-lft-out`
11×	`add-log-exp`
8×	`tan-quot` `add-exp-log` `associate-/r/` `add-cbrt-cube`
6×	`pow1` `fma-def`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`flip3-+` `associate-r` `associate-l` `associate-/r*` `sum-log` `flip-+` `associate-/l/`
2×	`+-commutative` `frac-add`
1×	`cbrt-undiv` `frac-times` `associate-+r-` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

84.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
12.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
3.0ms	(+ (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series796.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
230.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
98.0ms	(+ (tan y) (tan z))
98.0ms	(* (tan y) (tan z))

simplify846.0ms

Counts

167 → 167

Iterations

Useful iterations: done (841.0ms)

Iter	Nodes	Cost
0	284	3983
1	674	3616
2	1912	3383
done	5000	3358

prune667.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan y)) (cbrt (tan y)))
0.6b	(cbrt (tan y))
0.6b	(cbrt (tan y))
0.6b	(cbrt (tan y))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

8.0ms	(* (cbrt (tan y)) (cbrt (tan y)))
1.0ms	(cbrt (tan y))
1.0ms	(cbrt (tan y))
1.0ms	(cbrt (tan y))

series546.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (cbrt (tan y)) (cbrt (tan y)))
131.0ms	(cbrt (tan y))
129.0ms	(cbrt (tan y))
138.0ms	(cbrt (tan y))

simplify1.1s

Counts

99 → 99

Iterations

Useful iterations: 3 (312.0ms)

Iter	Nodes	Cost
0	90	824
1	181	740
2	529	692
3	1715	651
done	5001	651

prune429.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (pow (* (tan y) (tan y)) 1/3) (cbrt (tan y)) (tan z))
0.3b	(* (tan y) (tan y))
0.6b	(cbrt (tan y))
15.5b	(pow (* (tan y) (tan y)) 1/3)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log`
6×	`pow-pow` `add-cbrt-cube`
5×	`tan-quot`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-exp` `prod-exp` `pow-sqr` `pow-prod-up`
1×	`frac-times` `pow-to-exp` `unpow-prod-down` `cbrt-div` `unpow1/3` `pow1/3` `associate-r/` `associate-l/` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma (pow (* (tan y) (tan y)) 1/3) (cbrt (tan y)) (tan z))
5.0ms	(* (tan y) (tan y))
1.0ms	(cbrt (tan y))
5.0ms	(pow (* (tan y) (tan y)) 1/3)

series530.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(fma (pow (* (tan y) (tan y)) 1/3) (cbrt (tan y)) (tan z))
41.0ms	(* (tan y) (tan y))
126.0ms	(cbrt (tan y))
173.0ms	(pow (* (tan y) (tan y)) 1/3)

simplify3.1s

Counts

90 → 90

Iterations

Useful iterations: 3 (654.0ms)

Iter	Nodes	Cost
0	141	818
1	288	694
2	963	610
3	3925	590
done	5000	590

prune339.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes281.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	22	26
done	22	26

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.1s	3884×	body	1280	valid
951.0ms	2024×	body	640	valid
388.0ms	8000×	pre	80	true
198.0ms	629×	body	320	valid
119.0ms	1169×	body	80	valid
63.0ms	294×	body	160	valid