Details

sample295.0ms

Algorithm

intervals

Results

155.0ms	128×	body	1280	valid
76.0ms	68×	body	640	valid
17.0ms	256×	pre	80	true
11.0ms	23×	body	320	valid
4.0ms	29×	body	80	valid
3.0ms	8×	body	160	valid

simplify151.0ms

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: 13.6b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.1b	(tan (+ y z))

rewrite50.0ms

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:

18.0ms	(+ x (- (tan (+ y z)) (tan a)))
19.0ms	(- (tan (+ y z)) (tan a))
8.0ms	(tan (+ y z))

series485.0ms

Counts

3 → 9

Calls

3 calls:

224.0ms	(+ x (- (tan (+ y z)) (tan a)))
172.0ms	(- (tan (+ y z)) (tan a))
88.0ms	(tan (+ y z))

simplify3.6s

Counts

81 → 81

Iterations

Useful iterations: done (3.6s)

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

prune362.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

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)))
0.3b	(* (tan z) (tan y))
0.3b	(* (tan y) (tan z))

rewrite147.0ms

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:

74.0ms	(* (+ (tan y) (tan z)) (cos a))
28.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
18.0ms	(* (tan z) (tan y))
22.0ms	(* (tan y) (tan z))

series1.5s

Counts

4 → 12

Calls

4 calls:

270.0ms	(* (+ (tan y) (tan z)) (cos a))
845.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
181.0ms	(* (tan z) (tan y))
162.0ms	(* (tan y) (tan z))

simplify1.7s

Counts

107 → 107

Iterations

Useful iterations: done (1.7s)

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

prune926.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`times-frac` `associate-/l*`
6×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`fma-def` `distribute-frac-neg` `associate-r` `associate-*l/`
2×	`tan-quot` `cbrt-undiv` `neg-sub0` `neg-mul-1` `flip3-+` `div-sub` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `distribute-lft-out`
1×	`+-commutative` `associate-+r-` `frac-2neg` `unsub-neg` `pow-prod-down` `frac-add` `clear-num` `associate-/r` `sum-log` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

20.0ms	(+ x (/ (- (fma (fma (tan z) (tan y) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))) (* (cos a) (fma (tan z) (tan y) -1))))
0.0ms	(fma (fma (tan z) (tan y) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))
41.0ms	(* (+ (tan y) (tan z)) (cos a))
27.0ms	(/ (- (fma (fma (tan z) (tan y) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))) (* (cos a) (fma (tan z) (tan y) -1)))

series2.6s

Counts

4 → 12

Calls

4 calls:

981.0ms	(+ x (/ (- (fma (fma (tan z) (tan y) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))) (* (cos a) (fma (tan z) (tan y) -1))))
499.0ms	(fma (fma (tan z) (tan y) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))
261.0ms	(* (+ (tan y) (tan z)) (cos a))
858.0ms	(/ (- (fma (fma (tan z) (tan y) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))) (* (cos a) (fma (tan z) (tan y) -1)))

simplify1.3s

Counts

105 → 105

Iterations

Useful iterations: 2 (298.0ms)

Iter	Nodes	Cost
0	200	3054
1	493	2930
2	1664	2651
done	5000	2651

prune801.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (log (exp (* (tan z) (tan y))))) (cos a)))
0.3b	(* (tan z) (tan y))
0.3b	(* (tan z) (tan y))
3.1b	(log (exp (* (tan z) (tan y))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`tan-quot`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`log-prod` `times-frac` `prod-exp` `log-pow` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `pow-prod-down` `associate-/r/` `-commutative` `unswap-sqr`
1×	`exp-prod` `flip3--` `exp-to-pow` `frac-2neg` `rem-log-exp` `clear-num` `associate-/r*` `flip--` `div-inv`

Counts

4 → 87

Calls

4 calls:

37.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (log (exp (* (tan z) (tan y))))) (cos a)))
34.0ms	(* (tan z) (tan y))
20.0ms	(* (tan z) (tan y))
9.0ms	(log (exp (* (tan z) (tan y))))

series1.2s

Counts

4 → 12

Calls

4 calls:

768.0ms	(/ (fma (+ (* (tan z) (tan y)) -1) (sin a) (* (+ (tan y) (tan z)) (cos a))) (* (- 1 (log (exp (* (tan z) (tan y))))) (cos a)))
126.0ms	(* (tan z) (tan y))
146.0ms	(* (tan z) (tan y))
192.0ms	(log (exp (* (tan z) (tan y))))

simplify3.1s

Counts

99 → 99

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	152	1807
1	335	1625
2	1005	1429
3	3794	1409
done	5000	1409

prune783.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes890.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	33
1	29	33
done	29	33

end0.0ms

sample11.4s

Algorithm

intervals

Results

6.9s	3921×	body	1280	valid
2.7s	1982×	body	640	valid
536.0ms	8000×	pre	80	true
429.0ms	698×	body	320	valid
227.0ms	1132×	body	80	valid
151.0ms	267×	body	160	valid