Details

sample460.0ms

Algorithm

intervals

Results

248.0ms	121×	body	1280	valid
78.0ms	65×	body	640	valid
28.0ms	256×	pre	80	true
21.0ms	18×	body	320	valid
10.0ms	41×	body	80	valid
6.0ms	11×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
34	2015
33	1949
32	1871
31	1805
30	1727
29	1661
28	1583
27	1517
26	1439
25	1373
24	1295
23	1229
22	1151
21	1085
20	1007
19	941
18	863
17	797
16	719
15	653
14	575
13	510
12	430
11	354
10	254
9	186
8	103
7	71
6	61
5	46
4	35
3	29
2	22
1	15
0	9

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.7b	(tan (+ y z))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
2×	`tan-sum` `associate-+r+` `sum-log` `sub-neg` `diff-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `flip-+` `flip--` `difference-of-squares`

Counts

3 → 42

Calls

3 calls:

19.0ms	(+ x (- (tan (+ y z)) (tan a)))
28.0ms	(- (tan (+ y z)) (tan a))
5.0ms	(tan (+ y z))

series485.0ms

Counts

3 → 9

Calls

3 calls:

216.0ms	(+ x (- (tan (+ y z)) (tan a)))
198.0ms	(- (tan (+ y z)) (tan a))
70.0ms	(tan (+ y z))

simplify2.3s

Counts

51 → 51

Iterations

Iter	Nodes
4	6148
3	1496
2	467
1	195
0	91

prune606.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

19×	`associate-*l/`
18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `tan-quot`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `times-frac` `pow-prod-down` `frac-add` `-commutative` `flip-+` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*r/` `associate-/r/`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-sub` `div-inv` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

29.0ms	(* (+ (tan y) (tan z)) (cos a))
12.0ms	(* (tan y) (tan z))
14.0ms	(* (tan y) (tan z))
57.0ms	(/ (- (* (+ (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:

223.0ms	(* (+ (tan y) (tan z)) (cos a))
123.0ms	(* (tan y) (tan z))
136.0ms	(* (tan y) (tan z))
693.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify689.0ms

Counts

108 → 108

Iterations

Iter	Nodes
2	2247
1	593
0	194

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`add-cube-cbrt`
15×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
10×	`pow1` `associate-l` `tan-quot`
9×	`associate-r`
8×	`associate-/r/`
5×	`associate-*l/` `div-inv`
4×	`flip3--` `flip--` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `div-exp` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `div-sub` `associate-*r/`
1×	`clear-num` `frac-2neg` `flip3-+` `frac-add` `flip-+` `distribute-lft-out` `associate-/l/`

Counts

4 → 143

Calls

4 calls:

36.0ms	(* (+ (tan y) (tan z)) (cos a))
49.0ms	(/ (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- 1 (* (tan y) (tan z)))) (cos a))
24.0ms	(* (tan y) (tan z))
26.0ms	(* (tan y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (+ (tan y) (tan z)) (cos a))
672.0ms	(/ (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- 1 (* (tan y) (tan z)))) (cos a))
155.0ms	(* (tan y) (tan z))
157.0ms	(* (tan y) (tan z))

simplify778.0ms

Counts

155 → 155

Iterations

Iter	Nodes
2	2207
1	708
0	285

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize136.0ms

Local error

Found 4 expressions with local error:

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

rewrite563.0ms

Algorithm

rewrite-expression-head

Rules

114×	`associate-*l/`
72×	`frac-times`
59×	`add-cbrt-cube` `add-exp-log`
57×	`pow1`
51×	`associate-*r/`
42×	`associate-/l/`
40×	`frac-sub`
36×	`flip3-+` `tan-quot` `cos-mult` `flip-+`
32×	`prod-exp` `cbrt-unprod`
26×	`pow-prod-down`
25×	`flip3--` `flip--`
17×	`associate-/r/`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-undiv` `div-exp`
5×	`associate-r` `associate-l`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`pow-plus`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `div-sub` `swap-sqr` `div-inv` `unswap-sqr`

Counts

4 → 188

Calls

4 calls:

25.0ms	(* (tan y) (tan z))
135.0ms	(* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
85.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
307.0ms	(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z))))))

series2.0s

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (tan y) (tan z))
229.0ms	(* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
122.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
1.6s	(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z))))))

simplify10.2s

Counts

200 → 200

Iterations

Iter	Nodes
2	13128
1	1736
0	450

prune4.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes893.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
2	47
1	47
0	33

end0.0ms

sample11.0s

Algorithm

intervals

Results

7.0s	3879×	body	1280	valid
2.3s	2001×	body	640	valid
626.0ms	8000×	pre	80	true
416.0ms	702×	body	320	valid
280.0ms	1135×	body	80	valid
112.0ms	283×	body	160	valid