Details

sample340.0ms

Algorithm

intervals

Results

148.0ms	118×	body	1280	valid
110.0ms	66×	body	640	valid
16.0ms	256×	pre	80	true
11.0ms	24×	body	320	valid
7.0ms	43×	body	80	valid
2.0ms	5×	body	160	valid

simplify7.2s

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	39	9
5	89	9
6	193	9
7	451	9
8	1380	9
9	4837	9
done	5001	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
2.5b	(tan (+ y z))

rewrite72.0ms

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:

37.0ms	(+ x (- (tan (+ y z)) (tan a)))
20.0ms	(- (tan (+ y z)) (tan a))
10.0ms	(tan (+ y z))

series502.0ms

Counts

3 → 9

Calls

3 calls:

226.0ms	(+ x (- (tan (+ y z)) (tan a)))
181.0ms	(- (tan (+ y z)) (tan a))
95.0ms	(tan (+ y z))

simplify920.0ms

Counts

81 → 81

Iterations

Useful iterations: done (917.0ms)

Iter	Nodes	Cost
0	128	1195
1	283	1011
2	1003	882
done	5000	795

prune301.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite442.0ms

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:

172.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
222.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
9.0ms	(+ (tan y) (tan z))
16.0ms	(* (tan y) (tan z))

series1.5s

Counts

4 → 12

Calls

4 calls:

619.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
544.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
151.0ms	(+ (tan y) (tan z))
137.0ms	(* (tan y) (tan z))

simplify1.9s

Counts

219 → 219

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	296	6641
1	702	5567
2	2728	5029
done	5000	4679

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.6b	(pow (+ (tan y) (tan z)) 3)
6.3b	(cbrt (pow (+ (tan y) (tan z)) 3))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`cbrt-prod`
13×	`add-cube-cbrt`
10×	`tan-quot`
8×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `cbrt-div` `fma-def` `flip3-+` `associate-r` `associate-l` `frac-add` `flip-+`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`+-commutative` `frac-times` `pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `sum-log` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

18.0ms	(+ (tan y) (tan z))
44.0ms	(* (tan y) (tan z))
26.0ms	(pow (+ (tan y) (tan z)) 3)
23.0ms	(cbrt (pow (+ (tan y) (tan z)) 3))

series615.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(+ (tan y) (tan z))
147.0ms	(* (tan y) (tan z))
184.0ms	(pow (+ (tan y) (tan z)) 3)
132.0ms	(cbrt (pow (+ (tan y) (tan z)) 3))

simplify2.3s

Counts

111 → 111

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	147	1260
1	428	1048
2	2322	970
done	5000	967

prune650.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin z))
0.3b	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
0.6b	(pow (+ (tan y) (tan z)) 3)
6.3b	(cbrt (pow (+ (tan y) (tan z)) 3))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-prod` `add-sqr-sqrt`
12×	`add-cube-cbrt`
8×	`unpow-prod-down` `cube-prod`
7×	`pow1`
6×	`cube-div`
5×	`prod-exp` `cbrt-unprod`
4×	`tan-quot` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `associate-r` `associate-l`
2×	`cube-mult` `flip3-+` `unpow3` `frac-add` `flip-+` `sin-mult` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `times-frac` `pow1/3` `pow-prod-down` `pow-exp` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `-commutative` `rem-cbrt-cube` `div-inv` `associate-/l/` `associate-/l*` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

23.0ms	(* (sin y) (sin z))
27.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
25.0ms	(pow (+ (tan y) (tan z)) 3)
13.0ms	(cbrt (pow (+ (tan y) (tan z)) 3))

series527.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin y) (sin z))
152.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
159.0ms	(pow (+ (tan y) (tan z)) 3)
155.0ms	(cbrt (pow (+ (tan y) (tan z)) 3))

simplify1.9s

Counts

116 → 116

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	188	1507
1	549	1293
2	3139	1129
done	5001	1118

prune901.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes325.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	21
1	22	21
done	22	21

end0.0ms

sample11.3s

Algorithm

intervals

Results

6.8s	3828×	body	1280	valid
2.3s	2000×	body	640	valid
754.0ms	8000×	pre	80	true
365.0ms	697×	body	320	valid
258.0ms	1173×	body	80	valid
163.0ms	302×	body	160	valid