Details

sample164.0ms

Algorithm

intervals

Results

88.0ms	109×	body	1280	valid
30.0ms	73×	body	640	valid
10.0ms	256×	pre	80	true
7.0ms	24×	body	320	valid
4.0ms	40×	body	80	valid
2.0ms	10×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize10.0ms

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))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `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 → 42

Calls

3 calls:

18.0ms	(+ x (- (tan (+ y z)) (tan a)))
16.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series301.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(+ x (- (tan (+ y z)) (tan a)))
120.0ms	(- (tan (+ y z)) (tan a))
52.0ms	(tan (+ y z))

simplify42.0ms

Counts

51 → 51

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	196	346
1	467	335
2	1316	334
3	5002	334
done	5002	334

prune144.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
2×	`+-commutative` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `flip3--` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

8.0ms	(+ (tan y) (tan z))
130.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
76.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
17.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (tan y) (tan z))
393.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
413.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
97.0ms	(* (tan y) (tan z))

simplify78.0ms

Counts

79 → 79

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	367	860
1	1074	821
2	3057	814
3	5001	814
done	5001	814

prune289.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)))

rewrite126.0ms

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×	`flip3-+` `frac-add` `flip-+`
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` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 92

Calls

4 calls:

34.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
15.0ms	(* (tan y) (tan z))
14.0ms	(* (tan y) (tan z))
59.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.0s

Counts

4 → 12

Calls

4 calls:

318.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
97.0ms	(* (tan y) (tan z))
98.0ms	(* (tan y) (tan z))
517.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify88.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	655	1689
1	3093	1518
2	5001	1501
done	5001	1501

prune480.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (cos a)))
0.3b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
44×	`tan-quot`
27×	`associate-*l/`
25×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
14×	`add-sqr-sqrt`
13×	`associate-*r/`
11×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/l/`
7×	`associate-r` `associate-l`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`cbrt-undiv` `flip3-+` `pow-plus` `div-exp` `frac-add` `associate-/r/` `flip-+` `unswap-sqr`
1×	`pow2` `frac-2neg` `div-sub` `swap-sqr` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 123

Calls

4 calls:

15.0ms	(* (tan y) (tan z))
14.0ms	(* (tan y) (tan z))
75.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (cos a)))
67.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series861.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (tan y) (tan z))
96.0ms	(* (tan y) (tan z))
551.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (cos a)))
119.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify90.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	699	1719
1	3567	1461
2	5001	1460
done	5001	1460

prune520.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes298.0ms

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	33	29
1	35	29
2	35	29
done	35	29

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.9s	3905×	body	1280	valid
845.0ms	2011×	body	640	valid
296.0ms	8000×	pre	80	true
216.0ms	717×	body	320	valid
93.0ms	1124×	body	80	valid
46.0ms	243×	body	160	valid