Details

sample391.0ms

Algorithm

intervals

Results

215.0ms	123×	body	1280	valid
63.0ms	63×	body	640	valid
46.0ms	27×	body	320	valid
26.0ms	256×	pre	80	true
6.0ms	30×	body	80	valid
5.0ms	13×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
34	2015
33	1949
32	1871
31	1805
30	1727
29	1661
28	1583
27	1517
26	1439
25	1373
24	1295
23	1229
22	1151
21	1085
20	1007
19	941
18	863
17	797
16	719
15	653
14	575
13	510
12	430
11	354
10	254
9	186
8	103
7	71
6	61
5	46
4	35
3	29
2	22
1	15
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
1.9b	(tan (+ y z))

rewrite47.0ms

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×	`expm1-log1p-u` `pow1` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`tan-sum` `sum-log` `sub-neg` `diff-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `flip-+` `flip--` `difference-of-squares`

Counts

3 → 75

Calls

3 calls:

16.0ms	(+ x (- (tan (+ y z)) (tan a)))
20.0ms	(- (tan (+ y z)) (tan a))
10.0ms	(tan (+ y z))

series409.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(+ x (- (tan (+ y z)) (tan a)))
178.0ms	(- (tan (+ y z)) (tan a))
85.0ms	(tan (+ y z))

simplify653.0ms

Counts

84 → 84

Iterations

Iter	Nodes
3	2061
2	649
1	284
0	131

prune966.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.3b	(* (tan y) (tan z))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

16.0ms	(+ (tan y) (tan z))
53.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
100.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
22.0ms	(* (tan y) (tan z))

series1.1s

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (tan y) (tan z))
327.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
498.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
146.0ms	(* (tan y) (tan z))

simplify2.5s

Counts

185 → 185

Iterations

Iter	Nodes
3	4927
2	1587
1	585
0	248

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

221×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
90×	`prod-diff`
44×	`difference-of-squares`
31×	`distribute-lft-out`
30×	`fma-neg`
22×	`distribute-lft-out--`
13×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`pow1` `flip3--` `div-inv` `flip--` `add-log-exp`
5×	`tan-quot` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `prod-exp` `associate-*r/` `cbrt-unprod`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 240

Calls

4 calls:

69.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y))))
197.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
15.0ms	(/ (* (sin y) (tan z)) (cos y))
13.0ms	(* (sin y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

337.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y))))
701.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
162.0ms	(/ (* (sin y) (tan z)) (cos y))
120.0ms	(* (sin y) (tan z))

simplify5.0s

Counts

252 → 252

Iterations

Iter	Nodes
3	7729
2	1968
1	724
0	311

prune4.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize103.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (tan z))
0.2b	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (sin y) (tan z)) (cos y)) 3))) (+ (* 1 1) (+ (* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y))) (* 1 (/ (* (sin y) (tan z)) (cos y))))) (- (tan a)))
0.3b	(* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y)))
0.3b	(pow (/ (* (sin y) (tan z)) (cos y)) 3)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-cbrt-cube` `add-exp-log`
23×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
17×	`prod-exp` `cbrt-unprod`
14×	`pow1` `cbrt-undiv` `div-exp`
10×	`associate-r` `associate-l`
7×	`unpow-prod-down` `cube-prod` `swap-sqr`
6×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-exp` `rem-cube-cbrt`
2×	`pow-prod-down` `associate-r/` `-commutative` `unswap-sqr`
1×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `unpow3` `associate-*l/` `tan-quot` `pow-sqr` `pow-prod-up` `fma-udef` `sqr-pow`

Counts

4 → 131

Calls

4 calls:

13.0ms	(* (sin y) (tan z))
0.0ms	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (sin y) (tan z)) (cos y)) 3))) (+ (* 1 1) (+ (* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y))) (* 1 (/ (* (sin y) (tan z)) (cos y))))) (- (tan a)))
33.0ms	(* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y)))
23.0ms	(pow (/ (* (sin y) (tan z)) (cos y)) 3)

series2.1s

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (sin y) (tan z))
1.6s	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (sin y) (tan z)) (cos y)) 3))) (+ (* 1 1) (+ (* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y))) (* 1 (/ (* (sin y) (tan z)) (cos y))))) (- (tan a)))
171.0ms	(* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y)))
173.0ms	(pow (/ (* (sin y) (tan z)) (cos y)) 3)

simplify1.9s

Counts

143 → 143

Iterations

Iter	Nodes
2	3368
1	760
0	254

prune3.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
2	33
1	33
0	26

end0.0ms

sample16.1s

Algorithm

intervals

Results

9.8s	3915×	body	1280	valid
3.4s	1991×	body	640	valid
1.0s	8000×	pre	80	true
786.0ms	696×	body	320	valid
510.0ms	1124×	body	80	valid
159.0ms	274×	body	160	valid