Details

sample450.0ms

Algorithm

intervals

Results

232.0ms	132×	body	1280	valid
68.0ms	65×	body	640	valid
62.0ms	256×	pre	80	true
16.0ms	22×	body	320	valid
8.0ms	33×	body	80	valid
3.0ms	4×	body	160	valid

simplify9.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	33	9
4	39	9
5	89	9
6	193	9
7	451	9
8	1380	9
9	4837	9
done	5001	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.9b	(tan (+ y z))

rewrite103.0ms

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:

43.0ms	(+ x (- (tan (+ y z)) (tan a)))
43.0ms	(- (tan (+ y z)) (tan a))
14.0ms	(tan (+ y z))

series621.0ms

Counts

3 → 9

Calls

3 calls:

256.0ms	(+ x (- (tan (+ y z)) (tan a)))
263.0ms	(- (tan (+ y z)) (tan a))
102.0ms	(tan (+ y z))

simplify1.4s

Counts

51 → 51

Iterations

Useful iterations: 3 (497.0ms)

Iter	Nodes	Cost
0	91	627
1	197	590
2	475	572
3	1729	570
done	5000	570

prune492.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

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

rewrite497.0ms

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:

277.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
19.0ms	(+ (tan y) (tan z))
167.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
31.0ms	(* (tan y) (tan z))

series1.9s

Counts

4 → 12

Calls

4 calls:

769.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
174.0ms	(+ (tan y) (tan z))
806.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
196.0ms	(* (tan y) (tan z))

simplify1.0s

Counts

79 → 79

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	154	1433
1	376	1362
2	1173	1304
done	5000	1291

prune766.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
4.7b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`tan-quot`
35×	`*-un-lft-identity`
25×	`add-cube-cbrt`
20×	`pow1` `times-frac`
12×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l/` `difference-of-squares`
10×	`frac-sub`
9×	`frac-times` `associate-r/` `associate-r` `associate-l` `associate-l/`
6×	`swap-sqr`
5×	`associate-/r*` `distribute-lft-out--`
4×	`associate-/l*` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 133

Calls

4 calls:

27.0ms	(* (tan y) (tan z))
29.0ms	(* (tan z) (tan z))
34.0ms	(* (tan y) (tan y))
113.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (tan y) (tan z))
65.0ms	(* (tan z) (tan z))
60.0ms	(* (tan y) (tan y))
420.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

simplify3.7s

Counts

145 → 145

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	219	2157
1	603	1963
2	3638	1827
done	5002	1817

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
0.2b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
0.2b	(* (sin y) (sin z))
0.2b	(* (sin y) (sin z))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`pow1` `cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
6×	`associate-r` `associate-l`
4×	`sin-mult` `add-log-exp`
2×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `-commutative` `div-inv` `associate-/l/` `associate-/l*` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

40.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
36.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
25.0ms	(* (sin y) (sin z))
26.0ms	(* (sin y) (sin z))

series569.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
191.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
93.0ms	(* (sin y) (sin z))
87.0ms	(* (sin y) (sin z))

simplify1.4s

Counts

96 → 96

Iterations

Useful iterations: 2 (271.0ms)

Iter	Nodes	Cost
0	95	1194
1	253	1172
2	1395	908
done	5001	908

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes906.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	19	18
done	19	18

end0.0ms

sample14.1s

Algorithm

intervals

Results

7.7s	3929×	body	1280	valid
3.8s	1975×	body	640	valid
766.0ms	8000×	pre	80	true
610.0ms	664×	body	320	valid
235.0ms	1160×	body	80	valid
118.0ms	272×	body	160	valid