Details

sample333.0ms

Algorithm

intervals

Results

191.0ms	127×	body	1280	valid
49.0ms	69×	body	640	valid
17.0ms	256×	pre	80	true
15.0ms	26×	body	320	valid
4.0ms	25×	body	80	valid
4.0ms	9×	body	160	valid

simplify165.0ms

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: 12.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.6b	(tan (+ y z))

rewrite90.0ms

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:

34.0ms	(+ x (- (tan (+ y z)) (tan a)))
44.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series545.0ms

Counts

3 → 9

Calls

3 calls:

236.0ms	(+ x (- (tan (+ y z)) (tan a)))
197.0ms	(- (tan (+ y z)) (tan a))
111.0ms	(tan (+ y z))

simplify4.0s

Counts

81 → 81

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	128	1195
1	274	1008
2	644	882
3	2382	793
done	5000	773

prune369.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

39.0ms	(* (+ (tan y) (tan z)) (cos a))
27.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
32.0ms	(* (tan z) (tan y))
25.0ms	(* (tan y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

254.0ms	(* (+ (tan y) (tan z)) (cos a))
825.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
161.0ms	(* (tan z) (tan y))
108.0ms	(* (tan y) (tan z))

simplify1.8s

Counts

107 → 107

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	196	1852
1	454	1756
2	1479	1548
done	5000	1536

prune760.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.3b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b	(pow (* (tan y) (tan z)) 3)

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
44×	`tan-quot`
23×	`add-exp-log` `add-cbrt-cube`
20×	`frac-times` `pow-prod-down`
14×	`associate-r/` `associate-l/`
13×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative`
2×	`pow-pow` `pow-plus` `pow-exp` `rem-cube-cbrt` `unswap-sqr`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `swap-sqr` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

16.0ms	(* (tan y) (tan z))
16.0ms	(* (tan y) (tan z))
90.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
27.0ms	(pow (* (tan y) (tan z)) 3)

series751.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (tan y) (tan z))
156.0ms	(* (tan y) (tan z))
187.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
250.0ms	(pow (* (tan y) (tan z)) 3)

simplify1.2s

Counts

136 → 136

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	161	1465
1	428	1163
2	1844	1096
done	5000	1086

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (tan z) (tan y))) (cbrt (* (tan z) (tan y))))
9.0b	(cbrt (* (tan z) (tan y)))
9.0b	(cbrt (* (tan z) (tan y)))
9.0b	(cbrt (* (tan z) (tan y)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

44×	`tan-quot`
33×	`cbrt-div`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

97.0ms	(* (cbrt (* (tan z) (tan y))) (cbrt (* (tan z) (tan y))))
14.0ms	(cbrt (* (tan z) (tan y)))
13.0ms	(cbrt (* (tan z) (tan y)))
10.0ms	(cbrt (* (tan z) (tan y)))

series1.1s

Counts

4 → 12

Calls

4 calls:

387.0ms	(* (cbrt (* (tan z) (tan y))) (cbrt (* (tan z) (tan y))))
233.0ms	(cbrt (* (tan z) (tan y)))
221.0ms	(cbrt (* (tan z) (tan y)))
272.0ms	(cbrt (* (tan z) (tan y)))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	122	1394
1	252	1297
2	635	1174
3	1960	1068
done	5000	1046

prune776.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes824.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	56
1	37	52
done	37	52

end0.0ms

sample11.4s

Algorithm

intervals

Results

5.7s	3854×	body	1280	valid
2.6s	1964×	body	640	valid
850.0ms	1161×	body	80	valid
724.0ms	8000×	pre	80	true
655.0ms	697×	body	320	valid
150.0ms	324×	body	160	valid