Details

sample384.0ms

Algorithm

intervals

Results

201.0ms	130×	body	1280	valid
83.0ms	54×	body	640	valid
21.0ms	256×	pre	80	true
11.0ms	17×	body	320	valid
10.0ms	46×	body	80	valid
4.0ms	9×	body	160	valid

simplify155.0ms

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

localize19.0ms

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))

rewrite63.0ms

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:

19.0ms	(+ x (- (tan (+ y z)) (tan a)))
23.0ms	(- (tan (+ y z)) (tan a))
13.0ms	(tan (+ y z))

series501.0ms

Counts

3 → 9

Calls

3 calls:

223.0ms	(+ x (- (tan (+ y z)) (tan a)))
207.0ms	(- (tan (+ y z)) (tan a))
71.0ms	(tan (+ y z))

simplify3.4s

Counts

81 → 81

Iterations

Useful iterations: done (3.4s)

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

prune345.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite440.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `sum-log`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

17.0ms	(+ (tan y) (tan z))
216.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
158.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
25.0ms	(* (tan y) (tan z))

series1.6s

Counts

4 → 12

Calls

4 calls:

167.0ms	(+ (tan y) (tan z))
640.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
672.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
165.0ms	(* (tan y) (tan z))

simplify1.8s

Counts

219 → 219

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	296	6641
1	659	5549
2	1645	5029
done	5000	4398

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1))
0.1b	(+ (tan y) (tan z))
0.1b	(+ x (+ (- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a)) 0))
0.2b	(- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a))

rewrite919.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
61×	`times-frac`
48×	`prod-diff`
22×	`distribute-lft-out`
17×	`add-log-exp`
16×	`fma-neg`
6×	`add-exp-log` `fma-def` `sum-log` `add-cbrt-cube`
5×	`tan-quot` `div-inv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`flip3-+` `associate-/r*` `flip-+` `associate-/l/`
2×	`+-commutative` `diff-log` `frac-add` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `associate-+l-` `associate-+r-` `sub-neg` `associate-+r+` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--`

Counts

4 → 159

Calls

4 calls:

35.0ms	(/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1))
16.0ms	(+ (tan y) (tan z))
739.0ms	(+ x (+ (- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a)) 0))
120.0ms	(- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a))

series2.1s

Counts

4 → 12

Calls

4 calls:

390.0ms	(/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1))
191.0ms	(+ (tan y) (tan z))
739.0ms	(+ x (+ (- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a)) 0))
764.0ms	(- (/ (+ (tan y) (tan z)) (fma (- (tan y)) (tan z) 1)) (tan a))

simplify4.3s

Counts

171 → 171

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	228	4803
1	526	4043
2	1393	3665
3	4830	3232
done	5000	3230

prune869.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin y) (cos z))
0.1b	(+ x (+ (- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (fma (- (tan y)) (tan z) 1) (* (cos y) (cos z)))) (tan a)) 0))
0.2b	(- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (fma (- (tan y)) (tan z) 1) (* (cos y) (cos z)))) (tan a))
0.2b	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (fma (- (tan y)) (tan z) 1) (* (cos y) (cos z))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
24×	`prod-diff`
15×	`add-exp-log` `times-frac` `add-cbrt-cube` `add-log-exp`
8×	`fma-neg`
6×	`pow1`
5×	`associate-*r/` `sum-log` `associate-/r/` `cos-mult` `div-inv` `distribute-lft-out`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `div-exp` `associate-r` `associate-l` `associate-/l*`
2×	`flip3-+` `diff-log` `flip-+` `associate-/l/` `distribute-lft-out--`
1×	`tan-quot` `+-commutative` `associate-+l-` `associate-+r-` `sub-neg` `associate-+r+` `flip3--` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `frac-sub` `sin-cos-mult` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 121

Calls

4 calls:

22.0ms	(* (sin y) (cos z))
1.5s	(+ x (+ (- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (fma (- (tan y)) (tan z) 1) (* (cos y) (cos z)))) (tan a)) 0))
277.0ms	(- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (fma (- (tan y)) (tan z) 1) (* (cos y) (cos z)))) (tan a))
97.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (fma (- (tan y)) (tan z) 1) (* (cos y) (cos z))))

series2.0s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin y) (cos z))
607.0ms	(+ x (+ (- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (fma (- (tan y)) (tan z) 1) (* (cos y) (cos z)))) (tan a)) 0))
817.0ms	(- (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (fma (- (tan y)) (tan z) 1) (* (cos y) (cos z)))) (tan a))
570.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (fma (- (tan y)) (tan z) 1) (* (cos y) (cos z))))

simplify2.0s

Counts

133 → 133

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	253	4673
1	641	4043
2	2220	3614
done	5001	3378

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes347.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	32
1	32	30
done	32	30

end0.0ms

sample11.4s

Algorithm

intervals

Results

6.9s	3941×	body	1280	valid
2.1s	1938×	body	640	valid
641.0ms	8000×	pre	80	true
449.0ms	680×	body	320	valid
221.0ms	1132×	body	80	valid
203.0ms	309×	body	160	valid