Details

sample289.0ms

Algorithm

intervals

Results

175.0ms	130×	body	1280	valid
48.0ms	54×	body	640	valid
13.0ms	256×	pre	80	true
8.0ms	17×	body	320	valid
8.0ms	46×	body	80	valid
3.0ms	9×	body	160	valid

simplify134.0ms

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	38	9
5	45	9
6	51	9
7	61	9
8	74	9
9	86	9
10	95	9
done	95	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize22.0ms

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))

rewrite60.0ms

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)))
26.0ms	(- (tan (+ y z)) (tan a))
15.0ms	(tan (+ y z))

series462.0ms

Counts

3 → 9

Calls

3 calls:

189.0ms	(+ x (- (tan (+ y z)) (tan a)))
201.0ms	(- (tan (+ y z)) (tan a))
72.0ms	(tan (+ y z))

simplify3.1s

Counts

51 → 51

Iterations

Useful iterations: 3 (256.0ms)

Iter	Nodes	Cost
0	91	627
1	196	590
2	453	572
3	1243	570
4	4659	570
done	5000	570

prune194.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite366.0ms

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:

13.0ms	(+ (tan z) (tan y))
211.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
109.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
30.0ms	(* (tan z) (tan y))

series1.5s

Counts

4 → 12

Calls

4 calls:

168.0ms	(+ (tan z) (tan y))
616.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
606.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
143.0ms	(* (tan z) (tan y))

simplify1.8s

Counts

79 → 79

Iterations

Useful iterations: 3 (881.0ms)

Iter	Nodes	Cost
0	155	1433
1	368	1362
2	969	1302
3	2581	1291
done	5000	1291

prune464.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan z)) (cbrt (tan z)))
0.6b	(cbrt (tan z))
0.6b	(cbrt (tan z))
0.6b	(cbrt (tan z))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 79

Calls

4 calls:

41.0ms	(* (cbrt (tan z)) (cbrt (tan z)))
10.0ms	(cbrt (tan z))
2.0ms	(cbrt (tan z))
2.0ms	(cbrt (tan z))

series734.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(* (cbrt (tan z)) (cbrt (tan z)))
148.0ms	(cbrt (tan z))
183.0ms	(cbrt (tan z))
190.0ms	(cbrt (tan z))

simplify1.9s

Counts

91 → 91

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	86	784
1	170	704
2	374	660
3	759	621
4	1815	616
done	5001	586

prune530.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite566.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1`
5×	`tan-quot`
4×	`times-frac`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `div-exp` `prod-exp` `sum-log` `cbrt-unprod` `flip-+` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `frac-times` `associate-+r-` `flip3--` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `-commutative` `frac-sub` `flip--` `div-inv` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

298.0ms	(+ x (- (/ (/ (+ (* (sin z) (cos y)) (* (cos z) (sin y))) (* (cos z) (cos y))) (- 1 (* (tan z) (tan y)))) (tan a)))
193.0ms	(- (/ (/ (+ (* (sin z) (cos y)) (* (cos z) (sin y))) (* (cos z) (cos y))) (- 1 (* (tan z) (tan y)))) (tan a))
27.0ms	(* (tan z) (tan y))
45.0ms	(/ (+ (* (sin z) (cos y)) (* (cos z) (sin y))) (* (cos z) (cos y)))

series1.3s

Counts

4 → 12

Calls

4 calls:

502.0ms	(+ x (- (/ (/ (+ (* (sin z) (cos y)) (* (cos z) (sin y))) (* (cos z) (cos y))) (- 1 (* (tan z) (tan y)))) (tan a)))
551.0ms	(- (/ (/ (+ (* (sin z) (cos y)) (* (cos z) (sin y))) (* (cos z) (cos y))) (- 1 (* (tan z) (tan y)))) (tan a))
111.0ms	(* (tan z) (tan y))
178.0ms	(/ (+ (* (sin z) (cos y)) (* (cos z) (sin y))) (* (cos z) (cos y)))

simplify1.1s

Counts

90 → 90

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	191	2495
1	484	2391
2	1511	2207
done	5001	2183

prune531.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes295.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	27
1	23	27
done	23	27

end0.0ms

sample9.5s

Algorithm

intervals

Results

5.4s	3941×	body	1280	valid
2.4s	1938×	body	640	valid
473.0ms	8000×	pre	80	true
328.0ms	680×	body	320	valid
228.0ms	1132×	body	80	valid
99.0ms	309×	body	160	valid