Details

sample175.0ms

Algorithm

intervals

Results

102.0ms	126×	body	1280	valid
24.0ms	53×	body	640	valid
12.0ms	256×	pre	80	true
7.0ms	25×	body	320	valid
4.0ms	47×	body	80	valid
1.0ms	5×	body	160	valid

simplify108.0ms

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: 15.1b

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))
2.8b	(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))

series316.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(+ x (- (tan (+ y z)) (tan a)))
124.0ms	(- (tan (+ y z)) (tan a))
60.0ms	(tan (+ y z))

simplify1.6s

Counts

81 → 81

Iterations

Useful iterations: done (1.6s)

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

prune252.0ms

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	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.1b	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.3b	(* (tan y) (tan z))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

3.0ms	(+ (tan y) (tan z))
53.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
12.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
5.0ms	(* (tan y) (tan z))

series859.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (tan y) (tan z))
420.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
234.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
103.0ms	(* (tan y) (tan z))

simplify1.1s

Counts

181 → 181

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	244	4754
1	579	3963
2	1845	3544
done	5000	3509

prune615.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))
0.2b	(/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))
0.2b	(/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z))))
0.3b	(* (tan y) (tan z))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

495×	`times-frac`
414×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
305×	`add-cube-cbrt`
186×	`prod-diff`
62×	`fma-neg`
56×	`associate-/r/`
52×	`distribute-lft-out`
39×	`tan-quot`
23×	`associate-/r*` `div-inv`
19×	`add-exp-log`
17×	`flip3-+` `frac-add` `flip-+`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1`
6×	`associate-/l*` `add-log-exp`
5×	`difference-of-squares`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `associate-/l/` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `pow-flip` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 434

Calls

4 calls:

111.0ms	(- (/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))
10.0ms	(/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))
13.0ms	(/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z))))
5.0ms	(* (tan y) (tan z))

series1.1s

Counts

4 → 12

Calls

4 calls:

424.0ms	(- (/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))
294.0ms	(/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))
234.0ms	(/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z))))
106.0ms	(* (tan y) (tan z))

simplify2.3s

Counts

446 → 446

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	476	15748
1	1127	12635
2	3474	10561
done	5001	10489

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan z) (tan y))
0.1b	(- (* 1 (/ (+ (tan z) (tan y)) (- 1 (* (tan y) (tan z))))) (tan a))
0.1b	(/ (+ (tan z) (tan y)) (- 1 (* (tan y) (tan z))))
0.3b	(* (tan y) (tan z))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `prod-diff` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `associate-*r/` `frac-add` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

3.0ms	(+ (tan z) (tan y))
8.0ms	(- (* 1 (/ (+ (tan z) (tan y)) (- 1 (* (tan y) (tan z))))) (tan a))
12.0ms	(/ (+ (tan z) (tan y)) (- 1 (* (tan y) (tan z))))
5.0ms	(* (tan y) (tan z))

series870.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (tan z) (tan y))
424.0ms	(- (* 1 (/ (+ (tan z) (tan y)) (- 1 (* (tan y) (tan z))))) (tan a))
241.0ms	(/ (+ (tan z) (tan y)) (- 1 (* (tan y) (tan z))))
102.0ms	(* (tan y) (tan z))

simplify1.1s

Counts

111 → 111

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	201	1890
1	488	1724
2	1650	1640
done	5001	1629

prune451.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes596.0ms

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: 1 (1.0ms)

Iter	Nodes	Cost
0	15	20
1	21	18
2	23	18
done	23	18

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.2s	3982×	body	1280	valid
956.0ms	1980×	body	640	valid
381.0ms	8000×	pre	80	true
226.0ms	693×	body	320	valid
110.0ms	1076×	body	80	valid
57.0ms	269×	body	160	valid