Details

sample174.0ms

Algorithm

intervals

Results

89.0ms	109×	body	1280	valid
32.0ms	73×	body	640	valid
11.0ms	256×	pre	80	true
7.0ms	24×	body	320	valid
4.0ms	40×	body	80	valid
2.0ms	10×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5
done	260	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.2b	(tan (+ y z))

rewrite53.0ms

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:

17.0ms	(+ x (- (tan (+ y z)) (tan a)))
27.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series375.0ms

Counts

3 → 9

Calls

3 calls:

159.0ms	(+ x (- (tan (+ y z)) (tan a)))
148.0ms	(- (tan (+ y z)) (tan a))
68.0ms	(tan (+ y z))

simplify104.0ms

Counts

81 → 81

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3128	507
3	5001	488
done	5001	488

prune251.0ms

Pruning

8 alts after pruning (8 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	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 207

Calls

4 calls:

9.0ms	(+ (tan y) (tan z))
146.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
99.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms	(* (tan y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (tan y) (tan z))
454.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
480.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
114.0ms	(* (tan y) (tan z))

simplify84.0ms

Counts

219 → 219

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	676	4072
1	2087	3376
2	5001	3265
done	5001	3265

prune718.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-*l/`
16×	`tan-quot`
14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`frac-sub`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3--` `flip--`
8×	`pow1` `associate-/l/`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u`
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×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 102

Calls

4 calls:

34.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
15.0ms	(* (tan y) (tan z))
15.0ms	(* (tan y) (tan z))
62.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.2s

Counts

4 → 12

Calls

4 calls:

368.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
117.0ms	(* (tan y) (tan z))
118.0ms	(* (tan y) (tan z))
608.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify106.0ms

Counts

114 → 114

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	688	1785
1	3272	1583
2	5001	1572
done	5001	1572

prune594.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

38.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
15.0ms	(* (tan y) (tan z))
13.0ms	(* (tan y) (sin z))
319.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))

series1.1s

Counts

4 → 12

Calls

4 calls:

351.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
108.0ms	(* (tan y) (tan z))
76.0ms	(* (tan y) (sin z))
574.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))

simplify118.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	776	1871
1	3656	1657
2	5001	1652
done	5001	1652

prune623.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes339.0ms

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	32	22
1	32	22
done	32	22

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.1s	3905×	body	1280	valid
923.0ms	2011×	body	640	valid
375.0ms	8000×	pre	80	true
223.0ms	717×	body	320	valid
121.0ms	1124×	body	80	valid
51.0ms	243×	body	160	valid