Details

sample169.0ms

Algorithm

intervals

Results

96.0ms	123×	body	1280	valid
24.0ms	57×	body	640	valid
11.0ms	256×	pre	80	true
8.0ms	23×	body	320	valid
4.0ms	42×	body	80	valid
2.0ms	11×	body	160	valid

simplify77.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	22	9
3	31	9
4	37	9
5	47	9
6	54	9
7	64	9
8	82	9
9	99	9
10	107	9
done	107	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.3b	(tan (+ y z))

rewrite23.0ms

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:

9.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series329.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(+ x (- (tan (+ y z)) (tan a)))
131.0ms	(- (tan (+ y z)) (tan a))
60.0ms	(tan (+ y z))

simplify1.2s

Counts

81 → 81

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	128	1195
1	274	1008
2	644	882
3	2306	793
done	5000	792

prune264.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

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×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u`
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` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 102

Calls

4 calls:

12.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
22.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series1.1s

Counts

4 → 12

Calls

4 calls:

338.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
106.0ms	(* (tan y) (tan z))
107.0ms	(* (tan y) (tan z))
534.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify1.1s

Counts

114 → 114

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	207	2967
1	684	2770
2	2746	2374
done	5001	2369

prune594.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan y) (tan z))
0.3b	(* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
0.4b	(* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))
0.5b	(/ (- (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (sin a) (- 1 (* (tan y) (tan z)))))))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

472×	`associate-*l/`
148×	`tan-quot`
146×	`frac-times`
122×	`associate-/l/`
120×	`frac-sub`
98×	`flip3--` `flip--`
84×	`pow1`
72×	`flip3-+` `frac-add` `flip-+`
60×	`associate-*r/`
39×	`add-exp-log` `add-cbrt-cube`
35×	`pow-prod-down`
20×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity` `pow-sqr` `pow-prod-up`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `times-frac` `pow-plus` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `*-commutative`
2×	`pow2` `swap-sqr` `associate-/r/` `difference-of-squares`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`

Counts

4 → 270

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
25.0ms	(* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
37.0ms	(* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))
129.0ms	(/ (- (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (sin a) (- 1 (* (tan y) (tan z)))))))

series2.0s

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (tan y) (tan z))
188.0ms	(* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
172.0ms	(* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))
1.5s	(/ (- (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (fma (+ (tan y) (tan z)) (cos a) (* (sin a) (- 1 (* (tan y) (tan z)))))))

simplify616.0ms

Counts

282 → 282

Iterations

Useful iterations: done (596.0ms)

Iter	Nodes	Cost
0	466	14282
1	1623	12820
done	5000	12643

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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	(* (sin y) (tan z))
0.3b	(* (tan y) (tan z))
0.3b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

27×	`associate-*l/`
14×	`add-sqr-sqrt`
13×	`tan-quot` `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×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `associate-/r/` `-commutative` `unswap-sqr`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 100

Calls

4 calls:

11.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
4.0ms	(* (sin y) (tan z))
5.0ms	(* (tan y) (tan z))
28.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))

series1.0s

Counts

4 → 12

Calls

4 calls:

309.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
83.0ms	(* (sin y) (tan z))
97.0ms	(* (tan y) (tan z))
510.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: 2 (485.0ms)

Iter	Nodes	Cost
0	240	3075
1	775	2895
2	3110	2581
done	5000	2581

prune620.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes866.0ms

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	23	35
1	32	35
done	32	35

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.0s	3883×	body	1280	valid
1.2s	1976×	body	640	valid
360.0ms	8000×	pre	80	true
211.0ms	709×	body	320	valid
102.0ms	1126×	body	80	valid
61.0ms	306×	body	160	valid